This is a Phase I/II safety and efficacy study of COAST therapy in patients with advanced cancer for which no satisfactory therapy options exist. An initial Phase I cohort of 18-30 patients with advanced cancer will receive increasing components of the COAST regimen following a traditional 3+3 escalation design. The starting COAST combination includes hydroxychloroquine, sirolimus and metformin (DL1 - base combination). If this three-drug base combination is cleared for safety, two dose levels will be opened for enrollment exploring the safety of the base in combination with either dasatinib or nelfinavir. Patients will be assigned sequentially to DL2A (base + dasatinib) and DL2B (base + nelfinavir). If nelfinavir is deemed unsafe in combination with the base (DL2B is not cleared for safety, regardless of the safety of DL2A), no further drug combinations will be explored since all remaining combinations include nelfinavir. If both dasatinib and nelfinavir are individually safe in combination with the base (DL2A and DL2B are both cleared for safety), two additional dose levels will be explored, the first combining all five drugs and the second exploring nelfinavir at a higher dose. If dasatinib is not safe but nelfinavir is safe in combination with the base (DL2A but not DL2B cleared for safety), then only one additional dose level will be explored combining the base with a higher dose of nelfinavir. If neither DL2A nor DL2B are cleared for safety, then only the base combination may be considered safe. Once a given dose level is cleared for initial DLT evaluation (e.g., 0 of 3 patients have a DLT or at most 1 of 6 have a DLT), additional patients may be enrolled (i.e., 'backfilled') to that dose level while a higher dose level is being evaluated for safety. Prioritization for backfill will be given to dose levels proximal to the current dose level being explored, and to those dose levels with evidence of anti-tumor activity. Backfill patients who are DLT-evaluable will be included in making decisions on dose escalation. Accrual to a dose-level may be halted and additional patients enrolled to a lower dose level that was previously cleared for safety depending on the total number of DLTs observed among all DLT-evaluable patients at that lower dose level (initial and backfill patients). The maximum tolerated mixture is the highest dose level at which at most 1 of 6 patients experiences a DLT or, for a dose level sample size \>6 due to additional backfill patients, the highest dose level at which the observed DLT rate is ≤16.7%. The recommended phase 2 dose (RP2D) will be determined based on the totality of data, including the maximum tolerated mixture, dose adjustments, all safety data including any DLT-equivalent events (safety events that meet the criteria for a DLT regardless of treatment cycle and trial phase), and any response data. The study team may recommend a dose level lower than the maximum tolerated mixture as the RP2D based on their review of the data in aggregate. However, the RP2D will not exceed the dose level corresponding to the maximum tolerated mixture. The phase II efficacy trial will evaluate the anti-tumor activity of the COAST RP2D combination in patients with advanced prostate cancer based on a Simon two stage optimum design. The primary endpoint is the16-week PSA progression-free rate following treatment initiation, where PSA progression is defined per PCWG3. A maximum of 29 patients will be enrolled. In the first stage, 10 patients will be accrued. If none of the first 10 patients are PSA progression-free at 16 weeks, we will halt registration. If one or more patients are PSA progression-free at 16 weeks, an additional 19 patients will be enrolled. If 4 or more out of the 29 patients are PSA progression-free at 16 weeks, the treatment will be declared promising. This study is powered at 80% with a one-sided type I error rate of 5%. Specifically, this study has an 80% chance of declaring promise if the true 16-week PSA progression-free rate is at least 20%. If instead the true 16-week PSA progression-free rate is at most 5%, then the study has a 5% chance of declaring promise and a 60% chance of early termination. Phase I patients treated at the RP2D who meet inclusion and exclusion criteria for phase II will be included in the phase II cohort. Treatment will continue until there is 1) unacceptable toxicity (grade 3 or 4 toxicity that does not resolve to grade 1 or less by 28 days after drug withdrawal), 2) institution of new additional cancer therapy, 3) withdrawal of consent, 4) any condition that, in the opinion of the treating physician, renders continued COAST treatment to not be in the patient's best interest, 5) lack of compliance with study procedures by the patient, or 6) PSA progression by 16 weeks of COAST therapy.