For participants who receive therapeutic anticoagulation: stable anticoagulant regimen Not currently receiving anticoagulation therapy Need for anticoagulation Concomitant anticoagulation at therapeutic doses with oral anticoagulants or platelet inhibitors Current use of anticoagulation therapy INR ? . (unless receiving anticoagulation therapy). Subjects receiving anticoagulation therapy concomitant use of therapeutic anticoagulation Treatment with anticoagulation or antiplatelet agents, except for aspirin dosages of ? mg per day, within the last weeks For participants receiving therapeutic anticoagulation: stable anticoagulant regimen and stable INR during the days immediately preceding initiation of study treatment Requirement for chronic anticoagulation On anticoagulation and unable to discontinue temporarily Requires therapeutic doses of anticoagulants unless anticoagulation can be safely discontinued before surgery per standard practice (e.g. first deep vein thrombosis [DVT] for which anticoagulation has been at least months and repeat imaging demonstrates resolution of DVT) or an inferior vena cava (IVC) filter can be used in place of anticoagulation; subjects are permitted to resume anticoagulation following surgery per discretion of treating physician and/or site standard operating procedures (SOPs) Require therapeutic use of anticoagulation medications History or evidence of thrombotic disorders within months before first study treatment unless stable on anticoagulation for > months Patients on therapeutic or prophylactic anticoagulation will be excluded from enrollment on the protocol; however, patients can remain on the study if they develop a thrombosis that requires therapeutic anticoagulation during the course of protocol therapy Subject is actively on anticoagulation therapy. Subjects receiving anticoagulation therapy Patient has a bleeding disorder or a screening platelet count = . x ULN in patients not taking anticoagulation; patients on anticoagulation (e.g. enoxaparin, oral anticoagulants) are eligible regardless of PT/PTT; prior to biopsy, anticoagulation will be held per standard practice anticoagulation with inability to stop anticoagulants prior to surgery Is on anticoagulation that cannot be discontinued in the perioperative stage Requirement for anticoagulation treatment that increases INR or aPTT above the normal range (low dose DVT or line prophylaxis is allowed). Patients on anticoagulation therapy which cannot be held for metastatic biopsies Abnormalities in coagulation such as bleeding diathesis, or treatment with anticoagulants (that cannot be safely held for biopsy) that would preclude tumor and skin biopsies\r\n* For fulvestrant: ongoing anticoagulation that would preclude an IM injection\r\n* For tamoxifen: documented hypercoagulable state not receiving anticoagulation Unable or unwilling to take any prophylaxis; patients with history of or new/active deep vein thrombosis/embolism/thrombophilia are allowed to participate if they are on appropriate therapeutic anticoagulation during the treatment on the trial; these patients would not need the aspirin with the lenalidomide unless clinically indicated; therefore, patients must be able and willing to receive anticoagulation (prophylaxis versus therapeutic as clinically indicated) Patients receiving anticoagulation therapy are eligible if their INR is stable and within the recommended range for the desired level of anticoagulation Patients on therapeutic anticoagulation; Note: prophylactic anticoagulation (i.e. intraluminal heparin) for venous or arterial access devices is allowed Need for ongoing therapeutic anticoagulation Subject is receiving anticoagulation; washout period of days ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Chronic anticoagulation, not including aspirin, but including heparins, warfarin, oral anticoagulation or other platelet function inhibitors HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Chronic anticoagulation, not including aspirin, but including heparins, warfarin, oral anticoagulation or other platelet function inhibitors Patients receiving therapeutic non-Coumadin anticoagulation are eligible, provided they are on a stable dose (per investigator judgment) of anticoagulant Patients on therapeutic anticoagulation Patients requiring therapeutic anticoagulation with drugs requiring INR monitoring or anti-platelet therapy, except for acetylsalicylic acid (aspirin) ? mg per day, are not eligible Patients requiring therapeutic anticoagulation and irreversible platelet inhibitors (e.g. clopidogrel, prasugrel, or ticagrelor). Low dose aspirin for cardiac prophylaxis is allowed. Current use of anticoagulation; NOTE: use of low-dose anticoagulation medications (such as heparin) that are used to maintain the patency of a central intravenous catheter is allowed Patients with TE event occurring > months prior to enrollment and receiving active anticoagulation Patients requiring therapeutic anticoagulation Patients on therapeutic anticoagulation Note: prophylactic anticoagulation (i.e. intraluminal heparin) for venous or arterial access devices is allowed Patients must not be on any anticoagulation Therapeutic anticoagulation is not contraindicated, but for those patients on therapeutic anticoagulation, alteration in coagulation parameters is expected following initiation of dasatinib; for patients on therapeutic anticoagulation, coagulation parameters should be assessed weekly for the first cycle following initiation of dasatinib, weekly for the first cycle following a dose reduction, and weekly for a minimum of two weeks after stopping dasatinib Anticoagulation with Lovenox (enoxaparin) is permitted, however, patients on anticoagulation with warfarin are not permitted on this study Require therapeutic anticoagulation treatment, especially with Coumadin Concomitant anticoagulation, at therapeutic doses, with anticoagulants. Patients on oral anticoagulation therapy Patients receiving anticoagulation therapy are eligible if their INR is stable and within the recommended range for the desired level of anticoagulation In the absence of therapeutic intent to anticoagulate the patient: INR > . or PT > . xULN or aPTT > . xULN Therapeutic anticoagulation. For patients receiving therapeutic anticoagulation: stable anticoagulant regimen Chronic anticoagulation, not including aspirin, but including heparins, warfarin, oral anticoagulation or other platelet function inhibitors, that can not, in the documented opinion of the investigator, safely be interrupted from at least days prior to the initiation of the study regimen until after surgical resection of the tumor. Concurrent treatment with anticoagulation medication, unless approved by Sponsor Patients using oral or parenteral anticoagulation are not excluded provided they are on a stable dose of anticoagulant Therapeutic-dose anticoagulation must be discontinued and coagulation parameters must be normalized prior to the first dose of GSK and fulvestrant. Subject undergoing cardiothoracic surgery with anticoagulation must have anticoagulation reversed prior to target bleeding site (TBS) identification and treatment; Patients must not be receiving therapeutic anticoagulation Patients requiring anticoagulation or with uncontrolled bleeding are excluded Those who require therapeutic anticoagulation with coumarin-derivative anticoagulants Patients on active therapeutic anticoagulation Anticoagulation is permitted but patients may only be on lovenox for this purpose. Known coagulopathies, and those who require therapeutic anticoagulation with coumarin-derivative anticoagulants Active bleeding tendency; NOTE: patients on therapeutic anticoagulation should be monitored carefully to maintain therapeutic level of anticoagulation to avoid increased risk of bleeding due to concurrent drug induced thrombocytopenia; it is suggested that patients who require anticoagulation therapy while on therapy use low molecular weight heparin (LMWH) Concomitant anticoagulation with oral anticoagulants. Prothrombin time or INR =< . x ULN unless receiving therapeutic anticoagulation Patients on chronic anticoagulation such as Aspirin, Plavix, or Coumadin who cannot have anticoagulation held for procedures are not eligible If on anticoagulation, participant must be on stable therapeutic dose prior to enrollment Coagulopathy or anticoagulation therapy that cannot be safely corrected or interrupted for tumor biopsy Current use of therapeutic anticoagulation therapy Evidence of bleeding diathesis or coagulopathy; patients that are on anticoagulation therapy for deep vein thrombosis (DVT) will be allowed to enroll and continue on the treatment dose of enoxaparin or other anticoagulation such a warfarin Patients must not be on any anticoagulation Able to take required prophylactic anticoagulation. Institutional normalized ratio (INR) =< . x ULN (this applies only to patients who are not receiving therapeutic anticoagulation; patients receiving therapeutic anticoagulation should be on a stable dose) Activated partial thromboplastin time (aPTT) =< . x ULN (this applies only to patients who are not receiving therapeutic anticoagulation; patients receiving therapeutic anticoagulation should be on a stable dose) Active therapeutic anticoagulation Is receiving prophylactic or therapeutic anticoagulation with warfarin or any other oral anticoagulant Therapeutic anticoagulation Patients on fibrinolysis, full-dose therapeutic anticoagulation, or high dose antiplatelet therapy Continuous anticoagulation therapy; patients who were on anticoagulant therapy must complete a washout period of at least days and have confirmed normal coagulation parameters before study inclusion Patient receiving anticoagulation Use of therapeutic anticoagulation within days of surgery (not including venous thromboembolism prophylaxis) Active or recent (within prior months) thrombus, irrespective of anticoagulation status Documented venous thromboembolism while on therapeutic anticoagulation (anticoagulation failure) Currently receiving anticoagulation treatment Current oral steroid use or receiving daily therapeutic anticoagulation (e.g. Coumadin, Lovenox) Documented venous thromboembolism while on therapeutic anticoagulation (anticoagulation failure) Require chronic anticoagulation or anti-platelet therapy Women on anticoagulation Protein C deficiency (increased risk of skin necrosis do those on injectable anticoagulation) For patients receiving therapeutic anticoagulation: stable anticoagulant regimen Require chronic anticoagulation or anti-platelet therapy a condition requiring prolonged anticoagulation or anti-platelets Subjects on anticoagulation (other than aspirin) whom cannot have their anticoagulation held for the procedure due to other clinical reasons (i.e. recent cardiac stent placement) Subjects on anticoagulation (other than aspirin) whom cannot have their anticoagulation held for the procedure due to other clinical reasons (i.e. recent cardiac stent placement) Patients who require anticoagulation for whom biopsy would be contraindicated. Active therapeutic anticoagulation Patient receiving therapeutic anticoagulation Subjects requiring anticoagulation not eligible Require therapeutic use of anticoagulation medications