It will depend upon the present/proposed use of the adjoining space.
Set some furniture in the "take-away" area to get a feel of the finished room size.

A 4x7 closet is useless and space wasting as a walk in. There really isn't enough room, even if you attempt an L configuration. It would need to be a minimum of 7x7 to be able to have double hanging, and that presumes the door is in the dead center. Much better to have a 2'x7' well organized reach in closet where you can access everything. Reach in closets always utilize space better because the walkway to access the hanging items is in the room and does not have to be accounted for except in furniture placement.

oops, I got the size wrong; it is actually 4x12, with the possibility of being 7x12 if we angled it, but then it would NOT be a full rectangle...it would taper down to 4 ft. at the back of the closet.

I think it really matters what the finished room (the one getting smaller) will be, and its size. Can you post a layout? We can help you with it.

I have a 4 x 7 walk-in closet. Two 18" doors open outward on one 7' wall. There are two levels of hanging space on one 4' wall, one level on the other 4' wall and 3' of hanging space on the 7' wall opposite the door. That gives me a total of 15' of hanging space and 15' of shelf space. And it's all accessible space. To get the equivalent in a reach-in closet, I'd need 11 linear feet, and because of the door configurations, not all of the space would be easily accessible.