For an associative unital ring, properties of classes of modules of projective dimension bounded by some positive integer provides large insight to both the module category over the ring, as well as intrinsic properties of the ring itself. This is exemplified by many classical results, for example, Bass' characterisation of perfect rings, or, over a commutative noetherian local ring, the Auslander-Buchsbaum formula. In this talk, we will consider a higher analogue of Bass' theorem, that is, the relationship between the big finitistic dimension and properties of the class of modules of projective dimension at most n, denoted P_n, over a commutative ring. In particular, we are interested in properties of the direct limit closure of P_n and if P_n provides minimal approximations. This is related to a recent preprint with Michal Hrbek which characterises the commutative noetherian rings for which P_n is of finite type.