Is it possible to add apps to "Most Used" in the Start menu?

If so, could someone please show me how to do it? I removed a couple of apps from there and they either get replaced by a random program or disappear.

It's not possible, sorry.
Even on a third party start menu replacement, there won't be an option to add to the 'Most Used' folder.
The task bar really is the best place for your most popular/used programs.