This is a study of select drug therapies in patients with salivary gland cancer. The study has two phases: a molecular profiling phase (phase 1) and a treatment phase (phase 2).

Based on the Molecular profiling results in phase the participants will receive matched treatment if a specific aberration is identified or will receive treatment with Selinexor if unmatched and no druggable aberration is identified.

In molecular profiling phase of the study, participants will provide a sample of their tumor tissue to test for changes in certain genes that show whether certain drug treatments will be more useful than others.

Once participants have undergone molecular profiling, they will be offered a drug treatment depending on the results. Certain drug treatments are designed to target certain gene changes. If there is a matching drug treatment, participants will be offered that treatment (either outside a clinical trial or within a clinical trial). If there are no gene changes or there are changes to genes were there are no drug treatments available for those certain changes, participants will be offered the study drug, Selinexor.

Cancer is the uncontrolled growth of cells. Research shows that one way cancer cells can grow uncontrollably is when certain proteins, called exporter proteins, are present in high levels in the body. These proteins prevent certain other proteins important in protecting cells from becoming cancerous and important in the controlling the growth of cells, from working. The study drug Selinexor is new class of drug called Selective Inhibitor of Nuclear Export (SINE) that blocks the exporter proteins from working which may allow the other proteins to work and slow or stop tumors from growing.

Inclusion Criteria (Phase 1, Molecular Profiling):

• Have available archival tumor tissue or fresh tumor specimen from diagnostic histological tissue for molecular profiling.
• Histological or cytological proof of malignant salivary gland tumor
• ECOG performance score 0-2
• Documented evidence of recurrent or metastatic disease

Inclusion Criteria (Phase 2, Treatment):

• Interpretable result of molecular profiling in the molecular profiling phase of this study
• Advanced recurrent or metastatic salivary gland cancer for which no curative therapy exists
• Evidence of clinical or radiological disease progression at the time of study treatment
• At least one measurable target lesion as defined by RECIST 1.1
• Must have adequate hematological, liver, renal and cardiac function
• No concomitant use of drugs which may prolong QTc interval
• No history of serious cardiac illness
• No serious medical conditions that might be aggravated by treatment or limit compliance.
• Central nervous system metastases are permitted provided these are clinically stable
• Able to take oral medication and have no evidence of bowel obstruction, infectious/inflammatory bowel disease
• No other active malignancy at any other site
• 18 years of age or older
• Measureable disease as defined by RECIST v1.1
• Not receiving any other concurrent investigational agent
• If the matched treatment is in the context of another phase I trial, the eligibility criteria of the enrolled trial will be used instead of the criteria from this trial

Exclusion Criteria (Phase 1, Molecular Profiling):

• Refuses to have tumor tissue undergo molecular profiling
• Not enough tumor tissue for molecular profiling
• Life expectancy less than 3 months

Exclusion Criteria (Phase 2, Treatment):

• Had stopped the previous treatment but showed no clinical or radiological evidence of disease progression
• Have received the same drug treatment of assignment to the specific arm before the enrolment in to treatment phase (phase 2)