I have the exact same issue. We put a single towel bar in our tiny bathroom and hang two bath sheets, then have a couple hooks on the back of the door for additional towels that are in use.

If you are able, you may be able to add a basket or other container for small hand towels or washcloths on the back of the toilet.

Or... Maybe a small storage unit that would fit under your sink?

We cant even do that...we have a pocket door. I use a towel rack and we have a bar on the shower door. No place to put extras or guest towels!!

Here's another cool idea. You just have to make sure that you have attractive towels:)

There are some great looking cabinets that sit on the wall above your toilet. If you are not renting and it's a major issue then .....replace the sink with an in cabinet sink. Small sizes are available from the big box stores or you could have a custom cabinet designed.
I have also installed hotel racks - metal open shelving above the toilet which run from $49 to $299 depending on the quality.

How about some shallow shelves between two wall studs. Frame it out with some molding and you could even put a door on it if you wanted. You could make it as tall as the baseboard to ceiling measurement but of course only as wide as the space between two wall studs. I have also seen high shelves above the door molding to hold things like TP and other supplies. Use baskets or hang a curtain to hide the contents.

Are you able to hang some storage unit above the toilet ? how about over the door?