Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts above (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least of every cohort of patients with a solid tumor must be evaluable for hematologic toxicity, for Parts A and C; if dose-limiting hematologic toxicity is observed on either Part A or C, all subsequent patients enrolled must be evaluable for hematologic toxicity on that Part Patients with known bone marrow metastatic disease will be eligible for the study if they meet the following criteria: \r\n* Peripheral absolute neutrophil count (ANC) >= /mm^\r\n* Platelet count >= ,/mm^ (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions)\r\n* Hemoglobin >= . g/dL at baseline (may receive red blood cell [RBC] transfusions, provided they are not known to be refractory to RBC transfusions); these patients will not be evaluable for hematologic toxicity; at least of every cohort of patients must be evaluable for hematologic toxicity for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least of every cohort of patients must be evaluable for hematologic toxicity for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity Patients with known bone marrow metastatic disease will be eligible for study if they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least of every cohort of patients must be evaluable for hematologic toxicity for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled on Part A must be evaluable for hematologic toxicity Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least of every cohort of patients must be evaluable for hematologic toxicity for Part A, the dose escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least of every cohort of patients on Part A must be evaluable for hematologic toxicity for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity Patients with bone marrow metastatic disease who do not meet the above criteria will be eligible to enroll in the study with the following count criteria; these patients will not be evaluable for hematologic toxicity or hematologic dose limiting toxicity (DLT)\r\n* ANC > /uL within days prior to first dose of abemaciclib\r\n* Platelet count > ,/uL (may receive platelet transfusions) within days prior to first dose of abemaciclib\r\n* Hemoglobin >= . g/dL (may receive red blood cells [RBC] transfusions) within days prior to first dose of abemaciclib Absolute neutrophil count (ANC) >= /uL for subjects with bone marrow involvement; these subjects will not be evaluable for hematologic toxicity or hematologic dose limiting toxicity (DLT), but will be subject to dose modifications based on hematologic criteria Platelet count >= ,/uL (platelet transfusions allowed provided the patient is not known to be refractory to red cell or platelet transfusions) for subjects with bone marrow involvement; these subjects will not be evaluable for hematologic toxicity or hematologic DLT, but will be subject to dose modifications based on hematologic criteria Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts above (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least of every cohort of patients must be evaluable for hematologic toxicity for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts specified above (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least of every cohort of patients must be evaluable for hematologic toxicity for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity. Patients with solid tumors metastatic to bone marrow will be eligible for study but not evaluable for hematologic toxicity; these patients must not be known to be refractory to red cell or platelet transfusions; at least of every cohort of patients must be evaluable for hematologic toxicity; if dose limiting hematologic toxicity is observed at any dose level, all subsequent patients enrolled must be evaluable for hematologic toxicity Subjects with known bone marrow metastatic disease will be eligible for study provided they meet the specified blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these subjects will not be evaluable for hematologic toxicity; if dose-limiting hematologic toxicity is observed, all subsequent subjects enrolled must be evaluable for hematologic toxicity Adequate bone marrow function defined as:\t\r\n* Subjects with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these subjects will not be evaluable for hematologic toxicity; at least of every cohort of patients must be evaluable for hematologic toxicity for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent subjects enrolled must be evaluable for hematologic toxicity Patients with known bone marrow metastatic disease will be eligible for study as long as they meet hematologic function criteria; patients with marrow disease are not evaluable for hematologic toxicity All patients enrolled on the study must be evaluable for hematologic toxicity Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least of every cohort of patients with a solid tumor must be evaluable for hematologic toxicity, for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity All patients enrolled on Part A of the study must be evaluable for hematologic toxicity Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity Patients with lymphoma metastatic to bone marrow who have granulocytopenia, anemia, and/or thrombocytopenia will be eligible for study but not evaluable for hematologic toxicity (in Part A, there will be a maximum of one per cohort); such patients must meet the blood counts as in Part A (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled in Part A must be evaluable for hematologic toxicity