I see. I meant 'energetically accessible', but you mean more like 'affordably accessible' (in the sense that the molecular toolkit of a cell is what can 'afford' certain structures, due to chaperones available and so on).

Who knows what might be possible if you designed a cell from scratch - perhaps you could rework all the machinery to access other parts of fold space. After all, there are some weird and wonderful machines out there like the 'Vault' (https://en.wikipedia.org/wiki/Vault_(organelle)) that can fit whole proteins inside them. Possibly a different cage-like structure could help fold designed proteins into as-before unseen structures.