Patient with advanced or metastatic solid tumor and has disease progression after treatment with available therapies that are known to confer clinical benefit or who are intolerant to treatment that meets the following requirements for the part of the study they will participate in: Patients enrolled in Cohorts 1-5, Cohort A, Cohort B and Phase 2 Doublet must be refractory to all therapies known to confer clinical benefit to their disease. Diagnosis of advanced/metastatic solid malignancy for which no standard treatment option exists that will confer clinical benefit Histologically confirmed diagnosis of advanced unresectable or metastatic STS, not amenable to curative treatment and after available standard therapies have failed to provide clinical benefit. Note: Participants with a diagnosis of Grade 1 liposarcoma (atypical lipomatous neoplasms) are eligible if there is histological or radiographic evidence of evolution to more aggressive disease. Must have one of the following cancers, for which the patient has either received or been intolerant to all therapy known to confer clinical benefit Participants in all monotherapy arms must have an advanced solid tumor that has progressed on standard therapies known to provide clinical benefit or the participants are intolerant to such therapies. Participants must have an advanced solid tumor that has progressed on standard therapies known to provide clinical benefit or the participants are intolerant to such therapies. For all parts: The participant must be, in the judgment of the investigator, an appropriate candidate for experimental therapy after available standard therapies have failed to provide clinical benefit for their advanced or metastatic cancer. Patients who have an option for any treatment with proven clinical benefit for their lymphoid malignancy at current state of disease. Subjects with advanced solid tumors who are refractory to or intolerant of established therapy known to provide clinical benefit for their condition (i.e., subjects must not be candidates for regimens known to provide clinical benefit). Histologically or cytologically confirmed advanced TNBC that is relapsed, refractory, or progressive and not eligible for another standard therapy that would confer clinical benefit to the subject. Subjects must be refractory to or intolerant of existing cancer therapy(ies) known to provide clinical benefit. Men and Women > 18 years of age with Eastern Cooperative Oncology Group (ECOG) performance status < 2; 2a. Eligibility: U.S. Sites Includes subjects with loco-regional disease that have relapsed/recurred within 6 months of chemo-radiation and who have no standard of care. Includes patients (subjects) with metastatic disease having injections into only superficial lesions that have failed (includes progression, relapse or intolerance) or not be a candidate for approved therapies. Note, patients (subjects) that have approved therapies available, which might confer clinical benefit, may be enrolled as long as the physician properly explains the nature of the treatment, and obtains consent \. Includes patients (subjects) with metastatic disease having at least one deep tumor injection who have failed (includes progression, relapse or intolerance) all approved lines of therapy prior to enrollment unless they are not an appropriate candidate for a particular approved therapy or no approved therapy exists. Note: There is no limit on the number of prior therapies that a patient (subject) may have received prior to enrollment in any cohort. 2b. Eligibility: Canadian Sites Subjects with advanced or metastatic solid tumors that have disease progression after treatment with approved, available therapies (in site's country) for the cancer type or for whom available therapies have limited benefit and the subject refuses the available therapy. Includes subjects with locoregional disease that have relapsed/recurred within 6 months of chemo-radiation; or who have no standard of care or beneficial options. No limit on the number of prior treatments; Progression of tumor or intolerance to therapies known to provide clinical benefit. There is no limit to the number of prior treatment regimens Prior ruxolitinib treatment with failure to benefit or intolerance as defined by at least one of the following: Treatment with targeted agents, immunotherapy, or hormones is allowed; patients are only eligible if they have received and failed, or have been intolerant to standard treatments known to confer clinical benefit Cohort A: Patients with TNBC must have received no more than 4 lines of systemic cytotoxic chemotherapy; patients must have received and failed, or have been intolerant to anthracycline, taxanes, capecitabine, eribulin or other agents known to confer clinical benefit; patients are not required to fail all these agents if, in the investigator’s opinion, patients would benefit from treatment on current protocol HER2-expressing cancer as follows: Part 1: Any locally advanced (unresectable) and/or metastatic HER2-expressing (HER2 1+, 2+, or 3+ by IHC) cancer that has progressed after receipt of all therapies known to confer clinical benefit HER2-overexpressing (3+ by IHC) or HER2 2+ and FISH positive gastric cancer must have progressed after prior treatment with trastuzumab Part 2: ? Locally advanced (unresectable) and/or metastatic cancer that has progressed after receipt of all therapies know to confer clinical benefit (unless ineligible to receive a specific therapy) as follows: Has demonstrated clinical benefit from treatment with tazemetostat. Patients must be refractory to, or not a candidate for, established therapy known to provide clinical benefit for their malignancy. Patients with incurable malignancies, irrespective of 2-year mortality, who, in the opinion of the investigator have no treatment option expected to yield significant clinical benefit PART I: Recurrent or progressive disease on prior standard therapies with known clinical benefit with the exception of adjuvant bladder cancer population For the dose escalation portion of the trial, patients with available therapies known to confer clinical benefit (platinum sensitive ovarian cancer) must be excluded Patients with available therapies known to confer clinical benefit (platinum sensitive\r\nrecurrent ovarian cancer) must be excluded from the dose escalation portion Received at least one systemic therapy for advanced disease, with no further approved treatment options that provide proven clinical benefit. Refractory to or intolerant of existing therapy(ies) known to provide clinical benefit. Patients with metastatic bone sarcomas who have failed all available therapies that have demonstrated clinical benefit. Available therapies include but not limited to methotrexate, adriamycin and cisplatin for osteosarcoma and vincristine, adriamycin and cytoxan, ifosfamide, etoposide (VAC/IE) for Ewing’s sarcoma Patients demonstrating disease progression after treatment with available therapies that are known to confer clinical benefit, or who are intolerant to treatment, In the opinion of the Investigator would benefit from continued treatment. Patients must have exhausted all available therapies known to provide clinical benefit and has progressed, relapsed or is refractory to last line of treatment Refractory to or intolerant of existing therapy(ies) known to provide clinical benefit. For all arms except Arm G, subjects must be refractory to, or intolerant of, established therapy known to provide clinical benefit for their conditions, or where subjects refuse existing therapies. For Arm G, subjects must have newly histologically or cytologically confirmed diagnosis of locally advanced cervical cancer confined to the pelvis only. Patients who have received and failed, or have been intolerant to, standard first line therapies known to confer clinical benefit; patients who refuse standard therapy would also be eligible, as long as their refusal is documented Subjects with advanced or metastatic solid tumors that are refractory to standard therapies known to provide clinical benefit. Subjects with hematologic malignancy including lymphoma/myeloma will not be enrolled on this study. Disease not amenable to curative intent treatment (primarily surgery) and in addition has shown either clinical or radiographic progression on all available therapies known to confer clinical benefit Has B-cell lymphoma refractory to or intolerant of established therapy known to provide clinical benefit for their condition and having received rituximab as a single agent or in combination with other therapies. Patient has not received available therapies that confer clinical benefit a. Have advanced solid tumors that are refractory to established therapies known to provide clinical benefit for the malignancy in question, OR b. Be intolerant of established therapies known to provide clinical benefit for the malignancy in question Part 2: Subjects with HNSCC, NSCLC, pancreatic ductal adenocarcinoma, salivary gland cancer, and transitional cell carcinoma of the genitourinary tract that have had disease progression after available therapies for advanced or metastatic disease that are known to confer clinical benefit, have been intolerant to treatment, or have refused standard treatment. Patients demonstrating disease progression after treatment with approved therapies that are known to confer life-prolonging benefit, or who are intolerant to or have declined treatment Refractory to or intolerant of existing therapy(ies) known to provide clinical benefit. Progressive disease after failure of or intolerant to all available standard systemic treatments that have shown a documented benefit in overall survival for their respective tumor type. Patients must be refractory to, or intolerant of, existing therapies known to provide clinical benefit for their condition (i.e., cancer diagnosis). For dose-escalation portion of study, patients must be refractory to or intolerant of existing therapies known to provide clinical benefit for their condition. No other therapy with demonstrated clinical benefit in relapsed/refractory B-cell NHL available to the patient Patients must have advanced/metastatic solid malignancy or lymphoma for which no standard treatment option exists that will confer clinical benefit Response to first infusions:\r\n* Subjects who had a PR, or SD with clinical benefit may elect to receive a second infusion of cells; subjects that initially had a CR may only receive a second dose if evaluable disease recurs; clinical benefit is indicated by an improvement in the subject’s health status (eg, improved performance status or quality of life, decreased pain, etc.) For Part 1 and 2, subjects must have progressed following at least 1 line of prior therapy and there is no further established therapy that is known to provide clinical benefit (including subjects who are intolerant to the established therapy) Patients must have the potential for benefit from local therapy (at the discretion of the investigator) Phase I (Cohorts A through D, G, H, T, T2 and X): Histologically documented, locally advanced or metastatic solid malignancy or NHL that has progressed or failed to respond to at least one prior regimen and are not candidates for regimens known to provide clinical benefit Part 2: *Note: Subjects must have failed available therapies that are known to confer clinical benefit as indicated below, unless they are ineligible, intolerant, or refused standard treatment. Metastatic (Stage IV) or recurrent NSCLC (according to American Joint Committee on Cancer 7th edition guidelines) who have had disease progression after available therapies for advanced or metastatic disease that are known to confer clinical benefit, been intolerant to treatment, or refused standard treatment. Stage IV MSS CRC (according to American Joint Committee on Cancer 7th edition guidelines) who have had disease progression after available therapies for advanced or metastatic disease that are known to confer clinical benefit, been intolerant to treatment, or refused standard treatment. For all parts: The participant must be, in the judgment of the investigator, an appropriate candidate for experimental therapy after available standard therapies have failed to provide clinical benefit for their advanced or metastatic cancer. Patient is currently deriving clinical benefit from the study treatment, as determined by the investigator. are, in the judgment of the investigator, appropriate candidates for experimental therapy after available standard therapies have failed to provide clinical benefit Patients should not be eligible or able to receive approved therapy of confirmed clinical benefit in this patient population In the opinion of the investigator would benefit from systemic therapy Patients with a history of clinical benefit from prior RAF inhibitor therapy, as judged by the investigator, will be allowed For all Parts (Dose escalation and expansion): The participant must be, in the judgment of the investigator, an appropriate candidate for experimental therapy either after available standard therapies have ceased to provide clinical benefit (Parts A, B, C, D, E and F) or in combination with fulvestrant (Part G only) Patients who have progressive disease (PD) but have experienced \clinical benefit\ as defined in the study protocol Refractory to or intolerant of existing therapy(ies) known to provide clinical benefit for their condition. Histologically or cytologically confirmed B-cell NHL that has relapsed from, or is refractory to, standard therapies (including autologous transplantation) known to provide clinical benefit, but have not been treated with bendamustine for their lymphoma\r\n* Patients with limited exposure to Bendamustine (less than 2 full cycles) may be included, based on Principal Investigator (PI) discretion Documented clinical benefit following 6th cycle of DI-Leu16-IL2. Patients must have no available approved therapies that confer clinical benefit Response to previous RELHEM2 treatment: at least resistant disease with clinical benefit or better response Failed available therapy known to confer clinical benefit but no more than 4 prior lines of chemotherapy for metastatic disease. Absence of available therapy with reasonable likelihood of cure or significant clinical benefit Malignancies that are refractory to or intolerant of established therapy known to provide clinical benefit. Patients must not be candidates for anti-tumor regimes known to provide clinical benefit. Subject should be deriving clinical benefit without any persistent intolerable toxicity from continued treatment of ASP8273. Subjects not receiving clinical benefit from previous study therapy Advanced malignancy that is relapsed and/or refractory to all available therapies that will confer clinical benefit. Newly diagnosed patients who refuse standard treatment regimens are also eligible Rollover Cohort: Patients on active Hu5F9-G4 therapy on the Phase 1 AML (SCI-CD47-002) trial who are deriving clinical benefit by Investigator assessment Subjects who have disease progression after treatment with available therapies that are known to confer clinical benefit, or who are intolerant to treatment, or who refuse standard treatment. There is no limit to the number of prior treatment regimens. Subjects who have disease progression after treatment with available therapies that are known to confer clinical benefit, or who are intolerant to treatment, or subjects who refuse standard treatment