The two-step process of transfer followed by breakup is explored by measuring a rather complete set of exclusive data for reaction channels populating states in the ejectile continua of the $^7$Li+$^{93}$Nb system at energies close to the Coulomb barrier. The cross sections for $alpha+alpha$ events from one proton pickup were found to be smaller than those for $alpha+d$ events from one neutron stripping and $alpha+t$ events from direct breakup of $^7$Li. Coupled channels Born approximation and continuum discretized coupled channels calculations describe the data well and support the conclusion that the $alpha+d$ and $alpha+alpha$ events are produced by direct transfer to unbound states of the ejectile.
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