If I want to change my theme, but I've made many modifications to the template files, can I still change my theme while maintaining those changes?
What kind fo changes
*of. If its just plugins, unistall and then reinstall them. It usually works. If its CSS changes, you have to redo them.
It's PHP changes to the template files.
Just at your new theme to the template set. A template set can have multiple themes on it.
Really? Won't there be incompatibility problems?
Your template will remain the same, so the structure will remain the same, just the images and colour will be different.
*try it yourself
*add another theme to the template set