A flexible microscopic model is introduced in an attempt to illuminate problems associated with the calculation of single-nucleon-transfer form factors. The model employs a truncated shell-model basis augmented by a set of single-nucleon channels. It can be used even when the residual nucleus is unbound, but ignores contributions from many-particle breakup channels. The model wave function is fully antisymmetric, and it is shown that all quantities which appear in the model are calculable. An approximate single-channel calculation of form factors for the reactions 40Ca(d,p)41Ca(2.01 MeV) and 40Ca(3He,d)41Sc(2.10 MeV) is used to illustrate some of the features of the model.