Multiferroic materials are currently attracting a lot of interest because of the cross-coupling between their electrical and magnetic properties, which has the potential to lead to novel devices. There is a relatively small number of multiferroics currently known to exist and, hence, plenty of researches are devoted to design materials and phases possessing both ordered electric and magnetic dipoles. Here, we perform first-principles calculations on epitaxial (111) BiFeO3 films, and predict two novel stable multiferroic phases there. The first phase is the YMnO3-type hexagonal P63cm phase. It has an out-of-plane electrical polarization that anomalously increases when increasing the strength of the tensile epitaxial strain, and also possesses magnetic arrangements that are reminiscent of spin frustrations. The second phase adopts a P1 space group with a polarization having both out-of-plane and in-plane components, as well as, ferrimagnetism. These in-plane polarization and ferrimagnetism are both linked to a specific Fe-O bond, which is promising for inducing strong magnetoelectric coupling. The nature (i.e., improper versus proper) of the polarization in the P63cm and P1 phases will also be discussed.