I just installed SmartOptimizer: https://farhadi.ir/works/smartoptimizer
It is a php tool that does a few tricks to optimize your web site on the fly. Endorsed here (under its former name, jsmart).
When I tested the performance of my site using YSlow, my grade was raised from 47(F) to 81(B) – it compresses and minifies javascript and css, concatenates files, uses caching on both server and client side.
It might be worth a try – you have to be able to edit your .htaccess file as well as change permissions on directories.