I don't think it's possible. (And I feel your knee jerks kicking me already) But I wouldn't be opposed to a partial merger or 'strategic partnership' between GT and GStU. Wherein the Institute remains as a separate academic entity, but they share the non academic 'overhead' resources like- non-faculty admin staff, facilities, housing, and athletics- So, there's Georgia Tech and State University, where the 'I' and the 'U' are independent academic units...
Fold the GSU athletics into GT (GT has the better conference, brand, etc) All of a sudden the GTSU Yellow Jackets are an ACC program supported by 60,000+ undergrads and a lot of alumni. GSU isn't a great school, but it's a good school, R1 level research university and all that. Long term, I think such a school would end up like Michigan or Cal, a top 5 STEM school inside a major university.
Maybe even do a three-way trade that gets KSU the Perimeter College assets and GSU's Sunbelt spot. The BOR has been all about mergers and restructuring to cut costs and reduce redundancy. But, I know, they'd never go for this, because dwags.