Histologic documentation: pathologic confirmation of invasive breast cancer by core or surgical biopsy (fine-needle aspiration [FNA] alone is not adequate) Axillary lymph node positive breast cancer (fine needle aspiration [FNA] not required) Diagnosis confirmed on core needle, vacuum-assisted or surgery ? days of registration All patients must have had an axillary ultrasound with fine needle aspiration (FNA) or core needle biopsy of axillary lymph nodes documenting axillary metastasis at the time of diagnosis, prior to or at most days after starting neoadjuvant chemotherapy\r\n* Note: Biopsy of intramammary nodes does not fulfill eligibility criteria Surgical axillary staging procedure prior to study entry; Note: fine needle aspiration (FNA) or core needle biopsy of axillary node is permitted Patient must have had pathologic confirmation of axillary nodal involvement at presentation (before neoadjuvant therapy) based on either a positive fine needle aspirate (FNA) (demonstrating malignant cells) or positive core needle biopsy (demonstrating invasive adenocarcinoma); the FNA or core needle biopsy can be performed either by palpation or by image guidance; documentation of axillary nodal positivity by sentinel node biopsy (before neoadjuvant therapy) is not permitted Pathologic confirmation of metastatic breast cancer diagnosed by core needle biopsy Availability of archival or fresh tumor specimen that is suitable for analysis. Acceptable samples must have been acquired using core needle biopsy or excisional biopsy. Samples that were acquired using fine needle aspiration are not acceptable. Diagnosis of invasive ductal breast carcinoma by core needle biopsy, meeting the following criteria: Patients must have an adequate tumor tissue sample prior to enrollment available for correlative studies as defined below: core needle biopsy or incisional biopsy samples that can provide >= unstained sections of micron thickness; fine needle aspiration (FNA) sample alone is not sufficient The diagnosis of invasive adenocarcinoma of the breast must have been made by core needle biopsy. Nodal status - positive (FNA or core biopsy of the node[s] is cytologically or histologically suspicious or positive; Imaging is suspicious or abnormal but FNA or core biopsy was not performed.) The subject is willing to undergo a core needle biopsy during screening and during Cycle , Study Week . Archival tumor samples are requested, but are not required for eligibility. Histologic proof or unequivocal cytologic proof (fine needle aspiration, biopsy or two positive sputa) of SCLC within days prior to Step registration;\r\n* High-grade neuroendocrine carcinoma or combined SCLC and non-small cell lung cancer (NSCLC) is permitted Archival tumor sample available; tissue from an fine-needle aspiration (FNA) is allowed but tumor tissue from a core needle biopsy is preferred Histologic diagnosis of B-Cell NHL. Histology based upon bone marrow biopsies and/or fine needle aspirates as the sole means of diagnosis are not acceptable. All patients must have measurable disease. Any tumor mass of at least . cm is acceptable. Patients melanoma must be positive for both tyrosinase and human leukocyte antigen (HLA)-A per Loyola University Medical Center pathologic review from fine needle aspiration (FNA)/core/excisional biopsy of lesion Minor surgical procedures, fine needle aspirations or core biopsies within days prior to starting treatment; central venous catheter placements are permitted Be willing to provide tissue from an on-treatment fine-needle aspiration (FNA) or core biopsy of a tumor lesion; subjects must consent to on-treatment biopsy prior to initiation of clinical trial, however in subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may still continue on study Patients must have non-target lesion accessible for sequential biopsy (core needle biopsy or excision preferred, fine needle aspiration not eligible) STUDY TREATMENT: An adequate pre-treatment tumor biopsy is required to confirm histologic diagnosis. Acceptable options include laparoscopic biopsy or image-guided core needle biopsy (minimum of two cores). Fine needle aspiration (FNA) biopsy or cytology from ascites is not adequate. Liver lesion safely amenable to core needle biopsy. Willing to undergo core needle biopsy of liver metastatic site. Subject entering the study will need to consent for mandatory biopsy at study entrance and as an optional procedure prior to C for biomarker evaluation. Biopsy should be excisional, incisional or core needle. Fine needle aspiration is insufficient. Institutional confirmation of pathology on core biopsy (not cytology or fine needle aspiration) or laparoscopic biopsy performed at Memorial Sloan Kettering Cancer Center (MSKCC) with sufficient tissue for analysis, and willingness to undergo repeat biopsy if diagnostic biopsy was performed at an outside hospital Fine needle aspirate within days prior to study drug administration. Minor surgical procedures, fine needle aspirations or core biopsies within days prior to enrollment date. Bone marrow aspiration and/or biopsy are allowed. Have at least one metastatic lesion amendable for biopsy (core, punch, or fine needle aspiration [FNA]) The patient has a pathologic diagnosis of tumor biopsy or fine needle aspiration (FNA) of esophageal or gastric cancer of adenocarcinoma histology Willing to undergo a core needle or excisional biopsy on-treatment; subjects will be assessed at the time of biopsy for safety of undergoing the procedure Subject willing to undergo biopsy prior to treatment with investigational therapy for fresh tissue immune cell analysis and would consider biopsy at disease progression (progression biopsy is not mandated); biopsy should be obtained with core needle; fine needle aspirates are not sufficient; if prior archival tissue is available, it should be submitted Must agree to a fresh core or excisional biopsy from a metastatic site within a -week window prior to enrollment; if such a biopsy is already available, cell blocks must be provided; (Note: fine needle aspiration [FNA] and bone metastases samples are not acceptable for submission); specimens from the nephrectomy and fresh biopsy must be received and assessed for adequacy of tissue by the Data Coordinating Center (DCC) (University of Southern California [USC]) prior to randomization Consent to undergo a mandatory baseline biopsy of a metastatic tumor, if clinically feasible and safe to perform; acceptable samples include core needle biopsies of bone or lymph node; at least three cores should be obtained; a fine needle aspirate is not acceptable; subjects have the option of consenting to a repeat biopsy at time of progression Histologically proven invasive breast carcinoma (through either a core needle biopsy or an incisional biopsy) for which surgery is indicated as the primary treatment modality. Invasive adenocarcinoma of the breast diagnosed by core needle biopsy Ipsilateral axillary lymph nodes must be evaluated by MRI or ultrasound within weeks prior to study registration to determine clinical nodal status; if imaging is suspicious or abnormal, a fine needle aspiration (FNA) or core biopsy of the questionable node(s) on imaging is required; nodal status should be classified according to the following criteria:\r\n* Nodal status negative\r\n** Imaging of the axilla is negative; OR\r\n** Imaging of the axilla is suspicious or abnormal AND FNA or core biopsy is negative\r\n* Nodal status positive\r\n** FNA or core biopsy of node(s) is cytologically or histologically suspicious or positive Fine-needle aspiration (FNA) evidence of squamous cell carcinoma involving or more lymph nodes Histologic documentation of breast cancer by core needle or incisional biopsy Core needle biopsy or surgical specimen that confirms ICC; patients must be determined to be unresectable by a multidisciplinary team that includes a hepatobiliary surgeon Patient will have a tumor suitable for fine needle aspirates (FNA) or core biopsy for research purposes ( or more FNAs if core is not feasible) Pre-operative diagnosis or suspicion of papillary thyroid cancer, usually by fine needle aspiration (FNA) Unifocal primary invasive breast carcinoma diagnosed by core needle biopsy Minor surgical procedures, fine needle aspirations or core biopsies within days prior to day Fine needle aspirate within days prior to study drug administration Documented malignant biliary obstruction requiring endoscopic retrograde cholangiopancreatography (ERCP) guided stenting; documentation of malignancy will be made before the scheduled procedure and rapid pathology readings will not be used as a documentation of malignancy; documentation of malignancy may be in the form of;\r\n* Histology (bile duct biopsy)\r\n* Liver or pancreas fine needle aspiration (FNA), biliary\r\n* Brush cytology\r\n* Malignant ascites\r\n* Peritoneal biopsy\r\n* Cross sectional imaging (magnetic resonance imaging [MRI] or computed tomography [CT] scan) and abnormal liver function tests (findings compatible with obstruction) DCIS with microinvasion on histology on core needle biopsy Histological diagnosis must be based on surgical or core biopsy not just fine needle aspiration. Biopsies performed at other institutions must undergo pathology review and confirmation at MD Anderson Cancer Center. Have at least of the tumor sites that must be amenable to core needle biopsy and this may not be the site of disease used to measure antitumor response A tumor lesion that can be readily biopsied using a core needle via clinical exam or imaging-guidance Newly diagnosed and histopathologically confirmed (by central pathology review) potentially resectable soft tissue sarcomas of the extremity and trunk of the following subtypes: liposarcoma (excluding myxoid liposarcoma), leiomyosarcoma and undifferentiated pleomorphic sarcoma\r\n* An incisional or core biopsy is the preferred method for diagnosis; fine needle aspiration is not acceptable\r\n* Sites permissible for biopsy include\r\n** Extremities: upper (including shoulder) and lower (including hip)\r\n** Trunk: body wall Willing to undergo a baseline tumor core needle biopsy for correlative science studies; this study does not restrict eligibility based on PD-L expression Unilateral or bilateral primary carcinoma of the breast, confirmed histologically by needle core biopsy; fine-needle aspiration is not sufficient; incisional/excisional biopsy is not allowed; in case of bilateral cancer, the investigator has to decide prospectively which side will be evaluated for the primary endpoint MANDATORY biopsy after registration and prior to cycle day (CD) treatment: Primary tumor or a metastatic lesion must be amenable to biopsy after registration and prior to CD treatment for PD-L status and other correlative studies. Biopsy should be excisional, incisional or core needle. Fine needle aspiration is allowed as long as there is sufficient cellularity. Sample requirement is formalin-fixed paraffin-embedded (FFPE) block + H&E stained slides or unstained slides + H&E stained slide. Pathologic documentation of invasive breast cancer by biopsy (fine needle aspiration [FNA] alone is not adequate) The diagnosis of invasive adenocarcinoma of the breast must have been made by core needle biopsy Ipsilateral axillary lymph nodes must be evaluated by imaging (mammogram, ultrasound, and/or magnetic resonance imaging [MRI]) within weeks prior to randomization; if suspicious or abnormal, fine needle aspirate (FNA) or core biopsy is recommended, also within weeks prior to randomization; findings of these evaluations will be used to determine the nodal status prior to randomization:\r\n* Nodal status negative\r\n** Imaging of the axilla is negative\r\n** Imaging is suspicious or abnormal but the FNA or core biopsy of the questionable node(s) on imaging is negative\r\n* Nodal status positive\r\n** FNA or core biopsy of the node(s) is cytologically or histologically suspicious or positive\r\n** Imaging is suspicious or abnormal but FNA or core biopsy was not performed Palpable lymph nodes present in the supraclavicular areas or higher in the neck, unless proven to be benign on fine needle aspiration or biopsy Participants must have histological diagnosis consistent of Anaplastic Thyroid Cancer (ATC). Cytologic diagnosis by fine needle aspiration alone is not sufficient. Histologic diagnosis may be made by core needle biopsy, incisional biopsy, thyroidectomy, or other surgical biopsy. Fresh tumor biopsies (re-biopsy) should be obtained whenever feasible. The central pathology review may take place prior to or after the participant starts treatment with lenvatinib. Patients must be willing and able to undergo a biopsy after signed consent and prior to registration; patients must have tumor tissue and blood samples available and be willing to submit tumor and blood samples; NOTE: core biopsy required; fine needle aspiration (FNA) is not an acceptable substitute for core biopsy An archived tumor block or punches instead block must be available for submission for PD-L analysis. If an archived tumor block sample cannot be shipped for this study, then two mm punches from the core needle biopsy blocks may be provided for analysis. NOTE: core or excisional biopsy is required for this study. Fine needle aspirates (FNA) and cytology specimens are not adequate for PD-L analysis. A formalin fixed paraffin embedded lymph node or tumor biopsy specimen must be submitted during the Screening Period. The specimen must have been acquired by a surgical or core needle biopsy (? cores at baseline); material from a fine needle aspiration is not acceptable. Minor surgical procedures, fine needle aspirations or core biopsies within days prior to Day . Histologically confirmed invasive breast cancer by core needle or incisional biopsy (excisional biopsy is not allowed). Clinical stage T- N- or T N- by physical exam or radiologic studies. provide a newly obtained tumor tissue sample. Tumor tissue biopsies may be taken by surgical resection, core needle biopsy, or fine needle biopsy At least of the tumor sites must be amenable to core needle biopsy and this may not be the site of disease used to measure antitumor response Histologic diagnosis of unresectable or metastatic melanoma; for unknown primary disease, diagnosis of metastatic disease by cytology fine-needle aspiration (FNA) is not acceptable; BRAF wild-type confirmed, and NRAS mutation assessed Minor surgical procedures, fine needle aspirations or core biopsies within days prior to enrollment date; bone marrow aspiration and/or biopsy are allowed Patients with skin metastases must agree to tumor fine-needle aspiration (FNA) required by protocol Pathologically confirmed invasive breast cancer by core needle biopsy Surgical axillary staging procedure prior to study entry \r\n* Note: fine-needle aspiration (FNA) or core needle biopsy of axillary node is permitted Subject entering the study will need to consent for mandatory biopsy at study entrance and as an optional procedure at week and at progression for biomarker evaluation; biopsy should be excisional, incisional or core needle; fine needle aspiration is insufficient Diagnosis by fine needle aspiration (FNA) alone or excisional biopsy or lumpectomy performed prior to study entry. Patients who had a stereotactic needle biopsy Pathologically proven diagnosis of adenocarcinoma of the rectum (located below the peritoneal reflection or begins within cm of the anal verge on flexible endoscopy) within days of registration; diagnosis of rectal adenocarcinoma must be obtained by biopsy technique that does not completely excise the lesion (eg, fine needle aspiration, core needle biopsy) Fine needle aspirations or core biopsies =< days prior to registration/ randomization Fine needle aspirate within days prior to enrollment. STEP ENROLLMENT: the patient has a diagnosis of pathologically confirmed NSCLC by tumor biopsy and/or fine-needle aspiration; mixed tumors will be categorized by the predominant cell type STEP ENROLLMENT AND RANDOMIZATION: the patient has a diagnosis of pathologically confirmed NSCLC by tumor biopsy and/or fine-needle aspiration; mixed tumors will be categorized by the predominant cell type For stage I seminoma patients only, definitive surgical intervention within ten weeks prior to registration; patients undergoing scrotal violations (scrotal orchiectomy, transscrotal biopsy, testicular fine needle aspiration, scrotal exploration) will be eligible Definitive pathologic diagnosis by needle core biopsy Minor surgical procedures (needle/laparoscopic core biopsies) for limited purposes of tissue retrieval will be allowed; patients should not receive the first planned dose of bevacizumab until the wound is healed and days have elapsed since the procedure Provides a core needle biopsy consisting of at least separate tumor cores from the primary tumor at screening to the central laboratory. Patients with diagnosis by fine needle aspiration (FNA) cytology only Willingness to consent to the use of baseline diagnostic tumor specimen for correlative studies (any diagnostic material will be acceptable- paraffin block, cell block, fine needle aspirate etc.) Availability of archival diagnostic tissue (paraffin tissue block, cytospin block from a fine needle aspirate, or unstained slides from resected tumor, core biopsy, or fine needle aspirate) is required Histologic documentation of invasive breast cancer by core needle or incisional biopsy; excess baseline biopsy tumor tissue sufficient to make three -micron sections must be available for molecular analyses as part of this study Endoscopic ultrasound (EUS) with fine needle aspirate (FNA) for cytology Diagnosis of invasive adenocarcinoma of the breast made by core needle biopsy Tumor tissue from fine needle aspiration is not acceptable. Willing and able to undergo a post-dose core needle biopsy. Histologic diagnosis of unresectable or metastatic melanoma; for unknown primary disease, diagnosis of metastatic disease by cytology fine needle aspiration (FNA) is not acceptable Needle biopsy or incisional biopsy Previously treated, histologically confirmed cluster of differentiation (CD)+ B cell lymphoma; bone marrow biopsies as the sole means of diagnosis are not acceptable, but they may be submitted in conjunction with nodal biopsies or extra nodal biopsies; fine needle aspirates are not acceptable N- lymph node involvement based on positron emission tomography (PET)/endobronchial ultrasound-fine needle aspiration (EBUS-FNA)/mediastinoscopy (any N disease that is more than just minimal single station involvement is excluded) Histologically confirmed classical or lymphocyte predominant Hodgkin's lymphoma that is relapsed or refractory after at least one prior chemotherapy\r\n* Core-needle biopsies are acceptable if they contain adequate tissue for primary diagnosis and immunophenotyping\r\n* Bone marrow biopsies as the sole means of diagnosis are not acceptable, but they may be used in conjunction with nodal biopsies\r\n* Fine-needle aspirates are not acceptable\r\n* If the original diagnostic specimen is not available, specimens obtained at relapse may be utilized Exogenous sex steroid use within weeks prior to core needle biopsy Known regional malignant-appearing adenopathy or extra-biliary mass, indicating the need for concurrent endoscopic ultrasound with fine needle aspiration (EUS-FNA). Histologic proof or unequivocal cytologic proof (fine needle aspiration, biopsy, or two positive sputa) of small cell lung cancer (SCLC) Coaxial biopsy technique using Angiotech -gauge introducer needle Subjects with clinically/radiologically abnormal axillary lymph nodes should have pathological confirmation of disease with image guided biopsy/fine needle aspiration Willingness to undergo EUS with possible fine needle aspiration (FNA) Participants must have a diagnosis of DCIS made by core needle biopsy Women who were using oral contraceptives or postmenopausal hormones within eight weeks prior to core needle biopsy, and then stopped following core needle biopsy, are not eligible; use of hormone coated IUD like Mirena is allowed Prior or current random periareolar fine needle aspiration (RPFNA) evidence of atypia There has been a sufficient interval between a breast procedure and the RPFNA: at least months for a prior RPFNA, at least months for a core needle biopsy, at least months for an excisional biopsy Must be willing to undergo fine needle aspiration of breast adipose tissue at and months of the study Barriers to fine needle aspiration sampling of breast adipose, including breast implants, history of radiation to both breasts, bilateral mastectomies, and/or insufficient breast adipose tissue for adequate fine needle aspiration (FNA) sampling as determined by clinical examination and/or mammogram Surgical axillary staging procedure prior to first definitive breast operation; Note: fine-needle aspiration (FNA) or core needle biopsy of axillary node is permitted Patients must have an imaging abnormality that necessitated a core needle biopsy Patients must be registered on study within days after core needle biopsy Palpable abnormality diagnosed by core needle biopsy to be FEA or IPWA Patient registered on study more than days since the date of core needle biopsy Diagnosis of pathologically confirmed lung cancer by tumor biopsy and/or fine-needle aspiration Presence of a thyroid nodule that is amenable to ultrasound guided fine needle aspiration Patients with a diagnosis of breast cancer by either core needle biopsy or excisional biopsy Women with histologically confirmed breast cancer (by core needle biopsy) Subjects will have had standard care computed tomography (CT), MRI, or ultrasound, and a fine-needle aspiration biopsy demonstrating PTC or MTC with nodal metastases or recurrent/persistent nodal disease in a patient with known PTC or MTC Requiring tissue diagnosis (fine needle aspiration [FNA], core biopsy, surgical biopsy, surgical resection), or clinical follow-ups for at least months A core needle biopsy or fine-needle aspiration (FNA) is acceptable for diagnosis of metastatic disease in lymph nodes Patients who are candidates for thyroidectomy based on fine needle aspiration biopsy results of dominant (> . cm) thyroid nodules will be considered for study enrollment. Current hormone replacement therapy (HRT), selective estrogen receptor modulator (SERM) or aromatase inhibitor (AI) use; if yes, the wash-out period is days before diagnostic core needle biopsy\r\n* Note: local therapy (i.e. estrogen cream) will be permitted due to low systemic absorption of estrogen\r\n* Note: if patient is registered prior to completed washout, diagnostic core needle biopsy date will need to be provided