[Zeke]

It's not too hard to hang the outer doors and then hang the 2 inner ones to the outer ones. Sure, that sounds like another bifold but the secret is to reverse the hinges on the inner to outer door so that the inner door folds flat to the outer.
For full access, swing the pair open on the hinges mounted on the overall jamb that surrounds the opening.

You will need a different style of hinge for the outer doors, one that will clear any moldings. Theses are known a parliament hinges. I think you could also use a full clearance hinge on the outer. You might have to narrow the inner doors to 23 1/2".

Anyway, I've done it successfully.