Can supersymmetric loops correct the fermion mass relations in SU(5)?

We investigate possibilities for improving the fermion mass relations that arise in grand unified theories (GUTs). Each scenario relies on supersymmetric loop effects alone, without modifying the naive Yukawa unification. We briefly review the case where A terms follow the usual proportionality condition. In this case SUSY effects cannot completely improve the mass relations. Secondly, we employ a new ansatz for the trilinear A terms that satisfies all experimental and vacuum stability bounds, and can successfully modify the mass relations. Finally, we investigate the use of general (nonproportional) A terms, which can contain large off-diagonal entries. In this case, flavor changing neutral current (FCNC) data present an important constraint, but remedying the mass relations appears possible. We do not pretend to present a complete, motivated theory of fermion masses. Rather this paper can be viewed as an existence proof, serving to show that Yukawa coupling unification can occur even within the framework of minimal GUTs.