Mobile-only themes?

On our site, we use a custom them which does not scale or change (well) on mobile devices. Rather than update the entire theme to react to mobile browsers, we were hoping to find a pre-made solution.

We used Jetpack’s mobile theme for a while, but it didn’t work well with our site structure and it looked quite different from our main site.

My question is whether there exist themes which are mobile-only, or whether it is possible to activate two themes at once, using one for the standard site and one for the mobile.

Any help or suggestions appreciated. Thanks in advance.