History of grade 2 depression or anxiety or treatment with antidepressants, antipsychotics or monoamine oxidase inhibitor (MAO) inhibitors within 30 days of registration Prior exposure to approved receptor tyrosine kinase inhibitors is permitted; at least 5 half-lives must have elapsed since the completion of the kinase inhibitor and the initiation of study treatment Prior treatment with a BRAF inhibitor such as vemurafenib or dabrafenib (previous treatment with sorafenib is allowed) Prior treatment with cabozantinib (XL184) Prior treatment with cabozantinib Patients known to have Philadelphia chromosome positive (Ph+) ALL must have either failed treatment or been intolerant to treatment with at least one second or third generation tyrosine kinase inhibitor Prior treatment with selumetinib or another specific mitogen-activated protein kinase (MEK)1/2 inhibitor (unless the subject meets criteria for re-treatment) Study participants with a history of prior treatment with BRAF or MEK inhibitors Prior treatment on a CDK inhibitor Patients may have had treatment for no more than 2 prior relapses Patients may not have had prior treatment with mTOR, peptidase inhibitor 3, skin-derived (PI3) kinase or Akt inhibitors For all stage 2 participants, no prior treatment with mTOR, PI3 kinase or Akt inhibitors; prior treatment with mTOR, PI3 kinase or Akt inhibitors allowed in stage 1 only No prior treatment with crizotinib or another ALK inhibitor Patients may have had prior systemic therapy in the adjuvant setting; however this adjuvant treatment must not have included a CTLA4 or PD1 pathway blocking antibody or a BRAF/MEK inhibitor; also, patients may not have had any prior systemic treatment for advanced (measurable metastatic) disease Prior treatment with cabozantinib Patients who received prior PI3K, AKT or mTOR inhibitors are not allowed Prior treatment with selumetinib or another specific MEK 1/2 inhibitor Patients previously treated with an mammalian TOR (mTOR) or PI3K inhibitor No prior therapy with mTOR inhibitors except for rapalog treatment as part of graft-versus-host (GVH) prophylaxis or treatment PRIOR TO START OF TREATMENT: Prior treatment with a Hsp90 inhibitor PRIOR TREATMENT Prior treatment with pazopanib or any phosphoinositide 3-kinase (PI3K), mTOR, protein kinase B (AKT), or dual PI3K/mTOR complex (CREB regulated transcription coactivator [TORC]1/TORC2) inhibitors will be prohibited PRIOR/CONCURRENT THERAPY CRITERIA: Patients must not have received prior docetaxel; patients must not have received therapy with a drug known to be either a mitogen-activated protein kinase (MEK) inhibitor or a phosphatidylinositol 3 kinase (PI3K)/v-akt murine thymoma viral oncogene homolog 1 (AKT)/mammalian target of rapamycin (mTOR) pathway inhibitor Patients who have had prior therapy with any phosphatidylinositol 3 kinase (PI3K)/v-akt murine thymoma viral oncogene homolog 1 (AKT)/mammalian target of rapamycin (mTor) pathway inhibitor Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab Patients with prior treatment with PLD Patients requiring treatment with a receptor activator of nuclear factor kappa-B ligand (RANKL) inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab Prior treatment with selumetinib or another specific MEK 1/2 inhibitor Prior therapy with selumetinib or another specific mitogen-activated protein kinase kinase (MEK) inhibitor is not permitted Patients must not require treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab Previous treatment with XL184 (cabozantinib) or another MET/HGF inhibitor (tivantinib, crizotinib) Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab Refractory disease to treatment with an mTOR inhibitor Patient is INELIGIBLE if patient discontinued prior mTOR inhibitor due to toxicity Patient must NOT have had previous treatment with any PI3K or AKT inhibitor Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab Prior treatment with dasatinib, or any BCR-ABL1 inhibitor other than imatinib Patients must not have any prior treatment with any PI3K inhibitor, or lenalidomide Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab