Solid solutions BiMn1-xMxO3 with M = Al, Sc, Cr, Fe, and Ga and 0 <= x <= 0.2 were prepared at a high pressure of 6 GPa and 1333-1453 K, and their magnetic, thermal, and structural properties were investigated. The orbital-ordered monoclinic phase of BiMnO3 (phase I) is destroyed by a small percentage of substitution. The M elements can be classified by their ability to destroy phase I in the sequence Ga (x approximate to 0.08) approximate to Fe (x approximate to 0.08) < Cr (x approximate to 0.04) approximate to Al (x approximate to 0.04) < Sc (x approximate to 0.02), where phase I is most stable for Ga substitution (up to x approximate to 0.08) and less stable for Sc substitution (up to x approximate to 0.02). The orbital-disordered high-temperature monoclinic phase of BiMnO3 (phase II) is stabilized with larger x. In all cases, a compositional range was found where phases I and II coexist at room temperature. In phase I, the effect of substitution on the ferromagnetic transition temperature is weak (e.g., T-C = 102 K for BiMnO3 and T-C = 99 K for BiMn0.95Ga0.05O3), but there is a drastic effect on the orbital ordering temperature (e.g., T-OO = 474 K for BiMnO3 and T-OO = 412 K for BiMn0.95Ga0.05O3). Magnetic susceptibilities of phase I are typical for ferromagnets while, in phase II, ferromagnetic cluster-glass-like behavior is observed. The magnetic transition temperature of phase II (e.g., T-C = 70 K for BiMn0.8Ga0.2O3) exhibits a sudden drop compared with that of phase I. The effect of substitution on the structural monoclinic-to-orthorhombic transition is different depending on M (e.g., T-str = 768 K for BiMnO3, T-str = 800 K for BiMn0.95Ga0.05O3, and T-str = 738 K for BiMn0.85Cr0.15O3).