Well . . . Italian firms have a share in the EJ200 engine, a larger share (much of it through a UK subsidiary) in the CAPTOR radar, plus other fighter radars, including AESA, built by both the Italian & UK branches of that firm, & numerous other skills which would be valuable for a new fighter. They also have aerospace marketing & support networks worldwide. It's probably the best offer of co-operation Turkey has had so far.
We could imagine a mix of Eurofighter, OTS (Italian, Turkish & imported), & newly-developed Turco-Italian systems in a jointly-developed new airframe.
Juris praecepta sunt haec: honeste vivere, alterum non laedere, suum cuique tribuere.