I am brand new to the group and about to buy a 1st Gen for the first time since 1979. I sure wish I had kept just one of the five I once owned!

The car I am looking at has a crossmember/support that I have never seen, so I am looking for some help with what the purpose of this addition might be.

 

Definitely aftermarket,I'd expect it's to add some rigidity to the flexible flyers that these cars are.
I've never seen one like it but would assume it's somewhat like subframe connectors in purpose.

 

Thats a aftermarket, maybe Hotchkis or BMR, center brace used typically on convertibles. Its a good thing

 

+ 1 for that
Buy it

 

If I'm not mistaken, those supports are for convertibles, to give a bit more stiffness to the frame. The one in the pic is an aftermarket one to accommodate the larger exhaust.

 

yes Verts had a X brace. One in pic is aftermarket one. Likely Hotchkis or BMR. Good it has it