Patients with the following histologic epithelial cell types are eligible: serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, transitional cell carcinoma, malignant Brenner�s tumor or adenocarcinoma not otherwise specified (N.O.S.); however, the histologic features of the tumor must be compatible with a primary M�llerian epithelial adenocarcinomaXx_NEWLINE_xXPatients must have endometrial carcinoma including endometrioid adenocarcinoma, adenocarcinoma with squamous differentiation, mucinous adenocarcinoma, squamous cell carcinoma, mixed carcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, and serous adenocarcinoma histologiesXx_NEWLINE_xXPathologically (histologically) proven diagnosis of squamous cell carcinoma (including variants such as verrucous carcinoma, spindle cell carcinoma, carcinoma not otherwise specified [NOS], etc.) of the head/neck (oral cavity, oropharynx or larynx); note: hypopharynx primaries are excludedXx_NEWLINE_xXParticipant with histologic confirmation of newly diagnosed squamous cell carcinoma (SCC) of the head and neckXx_NEWLINE_xXPatient with sinonasal carcinomaXx_NEWLINE_xXPatient with nasopharyngeal carcinomaXx_NEWLINE_xXPathologically proven primary cervical cancer I-IIA with squamous cell carcinoma, adenosquamous carcinoma or adenocarcinoma initially treated with a standard radical hysterectomy with pelvic lymphadenectomyXx_NEWLINE_xXPatients with the following histologic epithelial cell types are eligible:* Serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, transitional cell carcinoma, malignant Brenner's Tumor, or adenocarcinoma not otherwise specified (N.O.S.) * However, the histologic features of the tumor must be compatible with a primary M�llerian epithelial adenocarcinoma; if doubt exists, it is recommended that the investigator should have the slides reviewed by an independent pathologist prior to entry * Patients may have co-existing endometrial cancer so long as the primary origin of invasive tumor is  ovarian or peritoneal for clarification of synchronous primary endometrial cancerXx_NEWLINE_xXOther invasive malignancy =< 5 years prior to registration; exceptions are colonic polyps, non-melanoma skin cancer, ductal carcinoma in situ, bladder carcinoma in situ, or carcinoma-in-situ of the cervixXx_NEWLINE_xXPatients with locally advanced, previously untreated squamous cell carcinoma of the vulvaXx_NEWLINE_xXPatients with a histologic diagnosis of squamous cell carcinoma, adenocarcinoma, or adenosquamous cell carcinoma of the cervix, stage IA1 (lymph-vascular space invasion [LVSI]+), IA2, and IB1 (tumor size [maximum visible or palpable]) =< 2 cm), any gradeXx_NEWLINE_xXPatients with other malignancies within the past 2 years, except for adequately treated carcinoma of the cervix or basal or squamous cell carcinomas of the skin or surgically treated early stage solid tumors are ineligible to participate in this studyXx_NEWLINE_xXSTEP I: Patients with a history of prior malignancy are eligible provided they were treated with curative intent and do not require active therapy (currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma �in situ� of the cervix or breast are not excluded)Xx_NEWLINE_xXHistory of non-breast malignancies (except for in situ cancers treated only by local excision and basal cell and squamous cell carcinomas of the skin) within 5 years prior to randomizationXx_NEWLINE_xXPrior malignancy within 2 years before enrollment other than curatively treated cutaneous basal cell or squamous cell carcinoma, carcinoma in situ of the cervix, anal intraepithelial neoplasia, or cutaneous Kaposi�s sarcoma (KS); participants with prior malignancies must have completed all therapy at least 2 years before enrollment with no evidence of disease since therapy completionXx_NEWLINE_xXPathologically proven diagnosis of a malignant major salivary gland tumor or malignant minor salivary gland tumor of the head and neck of the following histologic subtypes: * Intermediate-grade adenocarcinoma or intermediate-grade mucoepidermoid carcinoma* High-grade adenocarcinoma or high-grade mucoepidermoid carcinoma or salivary duct carcinoma* High-grade acinic cell carcinoma or high-grade (> 30% solid component) adenoid cystic carcinoma* Patients with diagnoses such as undifferentiated or poorly differentiated carcinoma, carcinoma-ex pleomorphic adenoma, carcinoma not otherwise specified (NOS) and others should be considered for this trialXx_NEWLINE_xXPatients must be disease-free of other prior invasive malignancies for >= 5 years with the exception of curatively-treated basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix; prior early stage breast cancers are also allowed as long as prior treatment did not include aromatase inhibitorsXx_NEWLINE_xXPatients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix, breast, or bladder; patients with prior malignancies must be disease-free for >= five yearsXx_NEWLINE_xXNo other malignancy within 5 years of registration with the exception of basal cell or squamous cell carcinoma of the skin treated with local resection only or carcinoma in situ of the cervixXx_NEWLINE_xXPresence of an invasive malignancy other than the study indication under this trial within 3 years of study enrollment except for carcinoma in situ CIS, squamous cell carcinomas of the skin, or basal cell carcinoma of the skin; a diagnosis of an invasive malignancy within 3 years is allowed if both the cure rate is felt to be > 80% and there has been no evidence of disease in the past yearXx_NEWLINE_xXPatients must have histologically or cytological confirmed malignancy in the following disease groups: melanoma that is metastatic or unresectable, non-small cell lung carcinoma, renal cell carcinoma, sarcoma, colon carcinoma, non-Hodgkin lymphoma, squamous cell head and neck carcinoma, or cutaneous squamous cell carcinoma, for which standard curative or palliative measures do not exist or are no longer effective; the primary site may be cutaneous or unknown, but mucosal and ocular primaries are excluded* Note: patients with non-small lung cancer must have had prior epidermal growth factor receptor (EGFR) and anaplastic lymphoma receptor tyrosine kinase (ALK) testing; patients with sensitizing mutations in EGFR or ALK rearrangements should have been treated with prior targeted agents and have had progression or discontinued due to toxicity from these agentsXx_NEWLINE_xXPatients in whom histologic diagnosis is not consistent with ductal adenocarcinoma such as adenosquamous, squamous cell, colloid, islet cell, serous or mucinous cystadenoma or cystadenocarcinoma, carcinoid, small or large cell carcinoma, intraductal oncocytic papillary neoplasms (IOPN), osteoclast-like giant cell tumors, acinar cell carcinoma, pancreatoblastoma, solid pseudopapillary tumors, undifferentiated small cell carcinoma and non-epithelial tumors (sarcomas, gastrointestinal [GI] stromal tumor, lymphoma)Xx_NEWLINE_xXPatients with the following tumors are included in the study:* Patients initially diagnosed with low-grade serous ovarian or peritoneal carcinoma that recur as low-grade serous carcinoma (invasive micropapillary serous carcinoma or invasive grade I serous carcinomas as defined by GOG, Federation of Obstetricians and Gynecologists [FIGO], World Health Organization [WHO] or Silverberg)* Patients initially diagnosed with serous borderline ovarian or peritoneal carcinoma that recur as low-grade serous carcinoma (invasive micropapillary serous carcinoma or invasive grade I serous carcinomas as defined by GOG, FIGO WHO or Silverberg)Xx_NEWLINE_xXPatients with a previous or current malignancy at other sites should be excluded, with the exception of:* Curatively treated local tumors such as carcinoma-in-situ of the cervix, basal or squamous cell carcinoma of the skin* Tumors for which no relapse has been observed within 5 yearsXx_NEWLINE_xXPatients must be disease-free of prior invasive malignancies for > 5 years with the exception of curatively-treated basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix* NOTE: If there is a history of prior malignancy, patients must not be receiving other specific treatment for that cancerXx_NEWLINE_xXPatients must have histologically proven urothelial carcinoma of the bladder; those with mixed histology, including a component of urothelial carcinoma, are eligible; small cell carcinoma, pure adenocarcinoma, and pure squamous cell carcinoma are excludedXx_NEWLINE_xXPatients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix, breast, or bladder; patients with prior malignancies must be disease-free for >= five yearsXx_NEWLINE_xXPatients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix, breast, or bladder; patients with prior malignancies must be disease-free for >= three years prior to registrationXx_NEWLINE_xXSolid tumor patients in stage 2 must have a diagnosis of papillary serous, endometrioid or clear cell endometrial carcinoma or, high grade serous, clear cell, endometrioid or mucinous ovarian, fallopian or primary peritoneal carcinomaXx_NEWLINE_xXNo concurrent malignancy other than non-melanoma skin cancer, superficial noninvasive (pTa or pT in situ [is]) transitional cell carcinoma (TCC) of the bladder, contralateral GCT, or intratubular germ cell neoplasia; patients with a prior malignancy, but at least 2 years since any evidence of disease are allowedXx_NEWLINE_xXPatients must not have other current malignancies, other than basal cell skin cancer, squamous cell skin cancer, in situ cervical cancer, ductal or lobular carcinoma in situ of the breastXx_NEWLINE_xXAdequately treated carcinoma in situ without current evidence of diseaseXx_NEWLINE_xXHas a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapyXx_NEWLINE_xXPatients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix, breast, or bladder; patients with prior malignancies must be disease-free for >= five yearsXx_NEWLINE_xXPatients with any component of small cell carcinoma are not eligible; other variant histologies are permitted provided the predominant (>= 50%) subtype is urothelial carcinomaXx_NEWLINE_xXPatients in the expansion portion must have:* Histologically confirmed diagnosis of metastatic:** Urothelial carcinoma of the bladder, urethra, ureter, renal pelvis, OR** Clear cell renal cell carcinoma OR** Adenocarcinoma of the bladder OR** Non-resectable squamous cell carcinoma of the penis OR** Squamous cell carcinoma of the bladder AND* Patients with urothelial cancer or renal cell carcinoma must have progressive metastatic disease defined as new or progressive lesions on cross-sectional imaging; patients must have at least:** One measurable site of disease (according to RECIST criteria) or bone disease by NaF PET/CTXx_NEWLINE_xXPatients must not have other current malignancies, other than basal cell skin cancer, squamous cell skin cancer, in situ cervical cancer, ductal or lobular carcinoma in situ of the breast; patients with other malignancies are eligible if they have been continuously disease-free for > 3 years prior to the time of randomizationXx_NEWLINE_xXPatients with brain metastases from primary germ cell tumors, small cell carcinoma, unknown primary, or lymphomaXx_NEWLINE_xXParticipant is =< 2 years free of another primary malignancy; exceptions include the following:* Basal cell skin cancer * Cervical carcinoma in situ* Anal carcinoma in situXx_NEWLINE_xXMust have a histologically confirmed transitional cell carcinoma (TCC, also known as urothelial carcinoma), locally advanced or metastaticXx_NEWLINE_xXHistory of non-breast malignancies (except for in situ cancers treated only by local excision and basal cell and squamous cell carcinomas of the skin) within 5 years prior to randomizationXx_NEWLINE_xXPatients with a history of another malignancy except for those who have been disease-free for 2 years; patients with a history of definitively treated non-melanoma skin cancer or squamous cell carcinoma of the cervix are eligible; patients with definitively treated in-situ cancers are eligible, regardless of timeframeXx_NEWLINE_xXDiagnosis or treatment for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, any in situ malignancy, or low-risk prostate cancer after curative therapyXx_NEWLINE_xXIf history of prior malignancy, subject should be in complete remission for >= 5 years at the time of registration (with the exception of basal cell or squamous cell carcinoma of the skin treated with local resection)Xx_NEWLINE_xXPatients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix, breast, or bladder; patients with prior malignancies must be disease-free for >= five yearsXx_NEWLINE_xXAny concomitant or prior invasive malignancies with the following curatively treated exceptions:* Treated limited stage basal cell or squamous cell carcinoma of the skin* Carcinoma in situ of the breast or cervix* Primary endometrial cancer meeting the following conditions: stage not greater than IA, grade 1 or 2, no more than superficial myometrial invasion, without vascular or lymphatic invasion; no poorly differentiated subtypes, including papillary serous/serous, clear cell, or other International Federation of Gynecology and Obstetrics (FIGO) grade 3 lesions* Prior cancer treated with a curative intent with no evidence of recurrent disease 3 years following diagnosis and judged by the investigator to be at low risk of recurrenceXx_NEWLINE_xXAny concomitant or prior invasive malignancies with the following curatively treated exceptions:* Treated limited stage basal cell or squamous cell carcinoma of the skin* Carcinoma in situ of the breast or cervix* Primary endometrial cancer meeting the following conditions: stage not greater than IA, grade 1 or 2, no more than superficial myometrial invasion, without vascular or lymphatic invasion; no poorly differentiated subtypes, including papillary serous/serous, clear cell, or other Federation of Gynecology and Obstetrics (FIGO) grade 3 lesions* Prior cancer treated with a curative intent with no evidence of recurrent disease 5 years following diagnosis and judged by the investigator to be at low risk of recurrenceXx_NEWLINE_xXPatients with active malignancies other than NSCLC or prior curatively treated malignancy at high risk of relapse during the study period with the exception of localized squamous or basal cell skin cancersXx_NEWLINE_xXPatients with concomitant or prior invasive malignancies within the past 3 years; subjects with treated limited stage basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the breast or cervix are eligibleXx_NEWLINE_xXPatients with active malignancies other than NSCLC or prior curatively treated malignancy at high risk of relapse during the study period with the exception of localized squamous or basal cell skin cancersXx_NEWLINE_xXPatients with previous or concomitant non-breast invasive malignancy; exceptions are limited exclusively to patients with the following previous malignancies, if adequately treated: basal or squamous cell carcinoma of the skin, in situ non-breast carcinoma, contra- or ipsilateral in situ breast carcinoma, stage Ia carcinoma of the cervixXx_NEWLINE_xXPatients with active malignancies other than NSCLC or prior curatively treated malignancy at high risk of relapse during the study period with the exception of localized squamous or basal cell skin cancersXx_NEWLINE_xXPatients with a history of any active malignancy requiring on-going treatment, except basal cell carcinoma or squamous cell carcinoma of the skinXx_NEWLINE_xXPatients with nasopharyngeal carcinoma, skin squamous cell carcinoma (SCC), and salivary gland carcinomas are not eligibleXx_NEWLINE_xXHistory of other prior malignancy, except squamous cell carcinoma of the cervix or anus, superficial basal cell or squamous cell skin cancer, or other malignancy curatively treated more than 5 years ago before enrollmentXx_NEWLINE_xXPathologically proven diagnosis of squamous cell carcinoma (including variants such as verrucous carcinoma, spindle cell carcinoma, carcinoma not otherwise specified [NOS]) of the head/neck (oral cavity, oropharynx, hypopharynx or larynx); pathologic stage III or IVA (American Joint Committee on Cancer [AJCC] 8): T3-T4a, N0-3, M0 or T1-T2, N1-3, M0Xx_NEWLINE_xXPrior systemic therapy for renal cell carcinomaXx_NEWLINE_xXDiagnosis of any second malignancy within the last 5 years prior to cycle 1, day 1, with the exception of those with a negligible risk of metastasis or death, per investigator�s discretion (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically with curative intent, ductal carcinoma in situ treated surgically with curative intent)Xx_NEWLINE_xXParticipant is < 2 years free of another primary malignancy; exceptions include basal cell skin cancer, stage 0-I squamous cell cancer of the skin, cervical carcinoma in situ, anal carcinoma in situXx_NEWLINE_xXInstitutional confirmation of Mullerian epithelial adenocarcinoma on core biopsy (not cytology or fine needle aspiration) or laparoscopic biopsy; (for phase II of the study formalin-fixed paraffin-embedded [FFPE] tissue should be available for laboratory analysis); patients with the following histologic epithelial cell types are eligible: high grade serous carcinoma, high grade endometrioid carcinoma, clear cell carcinoma, or a combination of theseXx_NEWLINE_xXPatients with mucinous carcinoma, low grade endometrioid carcinoma, low grade serous carcinoma or carcinosarcomaXx_NEWLINE_xXRectal cancer histology other than adenocarcinoma (i.e., sarcoma, lymphoma, squamous cell carcinoma, mucosal melanoma, etc.)Xx_NEWLINE_xXNo prior malignancy of any type (including ductal breast carcinoma in situ [DCIS]) within the past 5 years except for current diagnosis of breast cancer, and any prior diagnosis of basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix; patients with a prior history of breast cancer greater than 5 years from study screening may participate in this studyXx_NEWLINE_xXPatients must have recurrent or persistent endometrial cancer (endometrioid adenocarcinoma, serous adenocarcinoma, undifferentiated carcinoma, mixed epithelial carcinoma or adenocarcinoma not otherwise specified [NOS]); histologic confirmation of the primary tumor is requiredXx_NEWLINE_xXPatients must have histologically proven Ta, carcinoma in situ (CIS) or T1 stage urothelial cell carcinoma of the bladder within 90 days prior to registrationXx_NEWLINE_xXPatients must not have pure squamous cell carcinoma or adenocarcinomaXx_NEWLINE_xXPatients with mixed urothelial carcinoma and a glandular and/or squamous component will be eligible for the trial, but the presence of other histologic variants, pure adenocarcinoma, or pure squamous cell carcinoma, will make a patient ineligibleXx_NEWLINE_xXUpper age limit of =< 18 years of age for medullary thyroid carcinoma (MTC), renal cell carcinoma (RCC) and hepatocellular carcinoma (HCC)Xx_NEWLINE_xXPatients with a known concurrent malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or carcinoma in situ of the cervixXx_NEWLINE_xXPatients with a previous history of non-breast malignancy are eligible only if they meet the following criteria for a cancer survivor: (1), and (2)* Has undergone potentially curative therapy for all prior malignancies* Has been considered disease-free for at least 1 year (with the exception of basal cell or squamous cell carcinoma of the skin or carcinoma-in-situ of the cervix)Xx_NEWLINE_xXNo concurrent active malignancies are allowed on study for >= 2 years prior to treatment start with the exception of currently treated basal cell or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix or breastXx_NEWLINE_xXPatients with concomitant or prior invasive malignancies within the past 5 years; subjects with limited stage basal cell or squamous cell carcinoma of the skin, carcinoma in situ of the breast, or non-muscle invasive bladder cancer, are eligible as long as they received curative intent therapyXx_NEWLINE_xXPatients must not have poorly differentiated neuroendocrine carcinoma, high-grade neuroendocrine carcinoma, adenocarcinoid, goblet cell carcinoid and small cell carcinomaXx_NEWLINE_xXPatients with a history of acute myeloid leukemia (AML), or patients with a history of any other primary malignancy within 3 years prior to initiation of treatment on this study; exceptions include: patients with a history of malignancies (other than AML) that were treated curatively and have not recurred within 3 years prior to study entry; resected basal and squamous cell carcinomas of the skin; and completely resected carcinoma in situ of any typeXx_NEWLINE_xXPatient must be disease-free >= 3 years of prior malignancies with the exception of adequately treated non-melanoma skin cancer, adequately treated in situ carcinoma, low grade prostate carcinoma (Gleason grade =< 6) managed with observation that has been stable for at least 6 monthsXx_NEWLINE_xXPatient must have recurrent, persistent or metastatic cervical cancer including squamous cell, adenocarcinoma and adenosquamous histologies; mesonephric carcinoma, minimal deviation/adenoma malignum, clear cell carcinoma and gastric type are excludedXx_NEWLINE_xXMalignancies other than the cervical cancer within 5 years prior to cycle 1, day 1, with the exception of those with a negligible risk of metastasis or death, such as adequately controlled basal cell carcinoma or squamous cell carcinoma of the skin or carcinoma in situ of the breastXx_NEWLINE_xXHistologically-proven squamous cell carcinoma of the penisXx_NEWLINE_xXSquamous carcinoma of the urethraXx_NEWLINE_xXConcurrent malignancy (other than squamous cell carcinoma [SCC] or basal cell carcinoma of non-penile skin) that has required surgical or non-surgical treatment in the last 3 yearsXx_NEWLINE_xXConcurrent, active malignancies in addition to that being studied (other than cutaneous squamous cell carcinoma or basal cell carcinoma)Xx_NEWLINE_xXParticipants with any concomitant or prior invasive malignancies are ineligible with the following exceptions:* Treated limited-stage basal cell or squamous cell carcinoma of the skin* Carcinoma in situ of the breast or cervix* Prior cancer treated with curative intent with no evidence of recurrent disease 3 years following diagnosis and judged by the investigator to be at low risk of recurrenceXx_NEWLINE_xXIncluded tumor types* T cell and NK cell lymphomas, including, but not limited to: cutaneous T-cell lymphomas (CTCL), mycosis fungoides (MF), Sezary syndrome (SS), peripheral T-cell lymphoma (PTCL), ALK-positive and ALK-negative anaplastic large cell lymphoma (ALCL), and NK-cell lymphomas* Merkel cell carcinoma* Squamous cell carcinoma of the skin, including keratoacanthomas, vulvar squamous carcinoma, and mixed histology tumors, such as basosquamous carcinoma, and squamous cell carcinoma of unknown primary consistent with skin origin* Other non-melanoma skin cancers** Basal cell carcinoma** Malignant sweat gland tumors, including porocarcinoma, hidradenocarcinoma, spiradenocarcinoma, cylindrocarcinoma, microcystic adnexal carcinoma and related entities, squamoid eccrine ductal carcinoma, cutaneous adenoid cystic carcinoma, digital papillary adenocarcinoma, primary cutaneous mucinous carcinoma, endocrine mucin-producing sweat gland carcinoma, primary cutaneous signet ring cell carcinoma, cutaneous apocrine gland carcinoma, and extraocular sebaceous carcinoma** Adnexal carcinoma** Trichilemmal carcinoma** Extramammary Paget�s disease** Any other rare tumor of the skin with approval of principle investigator (PI)Xx_NEWLINE_xXPatients with invasive lobular carcinomaXx_NEWLINE_xXPatients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix, breast, or bladder; patients with prior malignancies must be disease-free for >= 5 yearsXx_NEWLINE_xXPatients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix, breast, or bladder; patients with prior malignancies must be disease-free for >= five yearsXx_NEWLINE_xXPatients with known active cutaneous squamous cell carcinoma (includes keratoacanthoma or mixed keratoacanthoma subtype) are not eligible; patients who have fully excised lesions with dermatologic confirmation of absence of disease are eligibleXx_NEWLINE_xX