It's not fixed, but there's a weird way of making what is basically a two-speed singlespeed: putting two freewheels on the rear hub and routing the chain in an unorthodox manner will give you a high gear ratio when pedaling forwards and a low ratio when pedaling backwards. The bike still coasts normally because of the freewheels, but you can not roll the bike backwards or rotate the pedals while stationary.

There are several pictures of my retro-direct conversion being built up here:
https://basementfreaks.com/gallery/ga...16898772e5dbdc

It seems to me that if you use a chain tensioner than you might be able to use a double or triple chain ring with a front changer to have a two or 3 speed fixed. Never having tried that I really don't know it may not shift properly or at all?

for truly fixed, it is not possible to have a chain tensioner because resisting will cause the tensioner to wind up and will slacken the upper part of the chain and cause nightmares.

If you were truly creative, you might find some way to have some kind of moveable fixed tensioner. I'm envisioning something that could be locked into place or released with a linkage of some kind. To shift rings, you would unlock the tensioner (so that it behaved like a typical spring-loaded tensioner or RD), shift the front on the fly, and then relock the tensioner to (hopefully) allow proper resisting without allowing the works to get gummed up.

A strong tensioner (steel cog on a bearing of some kind) mounted on a sturdy swinging arm could work if it had locking provisions. Perhaps a rod that goes from the tensioner arm up to the chainstay with a remotely-controllable locking mechanism to bite down on the sliding rod.

This would probably overcomplicate a fixed beyond the point of simplicity that so many like, but it just might work to allow multiple fixed gears without the rotational slop of a hacked SA hub conversion.

That's pretty slick, especially if you're going uphill and downhill a lot...I still wonder about that chainline though.