Phase IB Study to Evaluate the Safety of Selinexor (KPT-330) in Combination With Multiple Standard Chemotherapy or Immunotherapy Agents in Patients With Advanced Malignancies

Inclusion Criteria: * Patients must have histologically or cytologically confirmed malignant neoplasms (not including hematological malignancies and brain tumors) untreated or previously treated requiring further treatment; patients in Arm L (pembrolizumab), Arm M (nivolumab), and Arms N, O, P (nivolumab and ipilimumab) that have Food and Drug Administration (FDA)-approved indications for nivolumab, ipilimumab, and pembrolizumab do not have to fail first line nivolumab, ipilimumab, or pembrolizumab, and these patients may be treatment naïve if they have disease where pembrolizumab or nivolumab are FDA approved for the first-line setting * For all arms except Arm L (pembrolizumab), Arm M (nivolumab), and Arms N, O, P (nivolumab and ipilimumab) patients must have failed prior standard curative chemotherapy for their disease; subjects must have failed, be intolerant to, or be ineligible for any potentially curative approved treatment, irrespective of line of therapy * Patients must have measurable disease (Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.1) * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * The patient must be recovered from a prior major surgery; the major surgery must be performed at least 4 weeks prior to consent date * Platelets \>= 125 x 10\^9/L (For Arm L pembrolizumab, Arm M nivolumab and Arms N, O, P \[nivolumab and ipilimumab\] and expansion cohorts for all arms, platelets \>= 100 x 10\^9/L) * Hemoglobin \>= 10 g/dL (For Arm L pembrolizumab, Arm M nivolumab and Arms N, O, P \[nivolumab and ipilimumab\] and expansion cohorts for all arms, hemoglobin \>= 9 g/dL) * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (For Arm L pembrolizumab, Arm M nivolumab and Arms N, O, P \[nivolumab and ipilimumab\], ANC \>= 1.0 x 10\^9/L) * Transfusions and growth factors are allowed * Alanine transaminase (alanine aminotransferase \[ALT\]) =\< 2 x upper normal limit (ULN) (in the expansion cohort, patients with known liver involvement may have ALT =\< 5 x ULN); aspartate aminotransferase (AST) =\< 2 x ULN (in the expansion cohort, patients with known liver involvement may have AST =\< 5 x ULN) * Alkaline phosphatase \< 4 x ULN * Total bilirubin =\< 2 x ULN (in the expansion cohort, patients with Gilbert's syndrome \[hereditary indirect hyperbilirubinemia\] who must have a total bilirubin of =\< 3 x ULN) * Renal function defined as a calculated or measured glomerular filtration rate (GFR) \>= 30 mL/min. For patients with renal cell carcinoma (RCC), the GFR may be defined as \>= 25 mL/min * The patient has recovered to grade =\< 1 by the National Cancer Institute Common Terminology Criteria for Adverse Events, version 4.03 (NCI-CTCAE v4.03) from the effects of recent surgery, radiotherapy, chemotherapy, hormonal therapy, or other targeted therapies, with the exception of alopecia; the exceptions for such effects are allowed lab values of =\< grade 2 specified elsewhere in these inclusion criteria * Life expectancy of at least 12 weeks * Able to swallow and retain oral medication * Patients must give informed consent according to the rules and regulations of the individual participating sites * Negative serum pregnancy test in women of childbearing potential within 7 days of first dose of treatment and patients of child-bearing potential must agree to use effective contraception during/after 3 months post dose; a woman of childbearing potential is defined as a premenopausal female capable of becoming pregnant; this includes women on oral, injectable or mechanical contraception; women who are single and women whose male sexual partners have been vasectomized or whose male sexual partners have received or are utilizing mechanical contraceptive devices * For the Arm B (paclitaxel) expansion cohort, patients must have ovarian carcinoma, fallopian tube, or peritonea carcinoma * For Arm C (eribulin) expansion cohort, patients must have triple negative breast cancer (eribulin naive) * For Arm M (nivolumab) expansion phase, patients must have biopsiable disease * For the Arm N (nivolumab and ipilimumab), patients must have metastatic or unresectable renal cell carcinoma (RCC) * For the Arm O (nivolumab and ipilimumab) escalation and expansion Cohort O-1, patients must have metastatic or unresectable melanoma * For the Arm O (nivolumab and ipilimumab) expansion Cohort O-2, patients must have metastatic or advanced solid tumors (non-melanoma, non-renal cell carcinoma, or non- non-small cell lung carcinoma) * For the Arm P (nivolumab and ipilimumab), patients must have metastatic or unresectable non-small cell lung carcinoma (NSCLC) Exclusion Criteria: * Evidence of complete or partial bowel obstruction * Patients with primary central nervous system (CNS) tumor or CNS tumor involvement; however, patients with metastatic CNS tumors may participate in this study if the patient is: * \> 4 weeks from prior therapy completion (including radiation and/or surgery) * Clinically stable with respect to the CNS tumor at the time of study entry * Not receiving steroid therapy in treating CNS tumor or CNS tumor involvement * Not receiving anti-convulsive medications (that were started for brain metastases) * Need of total parenteral nutrition * Prior treatment with an agent targeting the exportin * Allergic to selinexor or any of the chemotherapy intended to receive * Pregnancy or lactation * Radiation (except planned or ongoing palliative radiation to bone outside of the region of measurable disease) =\< 3 weeks prior to study drug administration date * Chemotherapy, or immunotherapy or any other systemic anticancer therapy =\< 3 weeks prior to study drug administration date; patients receiving anti-PD-1 treatment, and continue to receiving this treatment in combination with selinexor (Arms L, M, N, O, and P), can start receiving the selinexor and anti-PD-1 combination without washout of the prior anti-PD-1 antibody * Diagnosis or recurrence of invasive cancer other than the present cancer within 3 years (except basal or squamous cell carcinoma of the skin that has been definitively treated) * Major surgery within four weeks before consent date * Unstable cardiovascular function: symptomatic ischemia (chest pain of cardiac origin), or uncontrolled clinically significant conduction abnormalities (e.g. ventricular tachycardia on antiarrhythmics are excluded and 1st degree atrioventricular \[AV\] block or asymptomatic left anterior fascicular block \[LAFB\]/right bundle branch block \[RBBB\] will not be excluded), or congestive heart failure (CHF) of New York Heart Association (NYHA) class \>= 3, or myocardial infarction (MI) within 3 months of consent date * Uncontrolled active infection requiring parenteral antibiotics, antivirals, or antifungals within one week prior to the first dose; active infection with concurrent treatment is acceptable only if the patient is clinically stable * Significantly diseased (as determined by the principal investigator \[PI\] or treating physician) or obstructed gastrointestinal tract or uncontrolled vomiting or diarrhea * Treatment with an investigational anti-cancer study drug within 3 weeks prior to study drug administration date * Concurrent therapy with approved or investigational anticancer therapeutics * Medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of the study results * Men whose partner is a woman of child-bearing potential, (i.e. biologically able to conceive), and who is not employing two forms of highly effective contraception; highly effective contraception (e.g. male condom with spermicide, diaphragm with spermicide, intra-uterine device) must be used by both sexes during the study and must be continued for 3 months after the end of study treatment; women of child-bearing potential is defined as sexually mature women who are not surgically sterile or who have not been naturally postmenopausal for at least 12 consecutive months (e.g., who has had menses any time in the preceding 12 consecutive months) * For Arms L (pembrolizumab) and M (nivolumab), and Arms N, O, P (nivolumab and ipilimumab), subjects with an active, known or suspected autoimmune disease; subjects with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll * For Arms L (pembrolizumab) and M (nivolumab), and Arms N, O, P (nivolumab and ipilimumab), subjects receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or other form of immunosuppressive therapy within 7 days before the first dose of study treatment; use of inhaled or topical steroids or systemic corticosteroids =\< 10 mg is permitted; in addition, physiologic steroid replacement with hydrocortisone is allowed * For Arms L (pembrolizumab) and M (nivolumab), and Arms N, O, P (nivolumab and ipilimumab), history of a prior grade 3 or 4 immune-related adverse event (irAE) or any grade ocular irAE from prior immunotherapy * For the Arm O (nivolumab and ipilimumab) expansion Cohort O-2, patients must not have melanoma, RCC, or NSCLC