Micro-transfer printing has demonstrated value for device- and array-level heterogeneous integration in a variety of applications. Here, it is used instead to assemble unique substrates with the potential to enable III-V growth templates that are both low-cost and specified at any desired lattice parameter within the range of III-V materials. Critical to this, epitaxial growth crystal quality must be established as comparable to that produced on conventional epi-ready substrates. We demonstrate epitaxial regrowth on gallium arsenide membranes that were transfer printed from their source substrate and onto a target handle. Both morphology and luminescence properties were characterized. Comparing the transfer printed membrane epitaxy with epitaxy on a conventional substrate, we found recombination rates and spatial uniformity from power-dependent photoluminescence and cathodoluminescence, respectively, to yield similar results, suggesting material quality was not adversely limited by the engineered substrate.