Do you have a picture?

Could you build out the wall some and put in a barn door? Or, a pocket door? Or double doors?

What exactly do you have?

Brass is back, FWIW.

Brass? My designer just told me the trend is oil rubbed bronze but she was talking about doorknobs, mine are 20-year old brass. Looks like I have another project.

ORB is on its way out in areas of the country. Do what YOU like.

Take a look here at a couple of solutions. One is painting the brass; the other is frosting the mirror. Both look terrific and updated.

Here is a link that might be useful: Closet door makeovers

There are many makeover solution and DIY guide that you can do with that. Brass looks an old era, why not change to something modern but unique, replacing is not solution but reinventing to something lovelier is possible.

Here is a link that might be useful: http://caldwells.com/interior-doors/closet-doors

Yep, brass is back. Congratulations on waiting long enough that you don't have to spend money updating it. I finally got rid of mine last year, so I'm sunk. :D

Seriously, the design mags and shows are pushing gold and brass like crazy.

It's supposed to be a different "shade" of brass, though, slightly more aged and not as shiny.

Maybe if you update other things in the room, you can make the brass look intentional? Would that be easier?

Here is a link that might be useful: Item #4

Brass and gold finishes are back, and I like brass and gold -- always have, but the typical shower glass enclosure frame and sliding glass door frame have never been among what I would consider attractive brass fixtures or features. More like a necessary evil at the time.
When we redo our closet doors, I have been thinking of something like this

They come in a number of styles, but I like the idea of frosted glass letting some light through - something you can't do by adding something on top of mirrored glass.