Category template to display posts from multiple categories

I’ve been looking for a solution to this for sometime (if one exists).

I need a category template which can display posts from multiple categories rather than just one. is there a way to do this without using a plugin.

I can do this using a page template i coded myself, but the problem is it does not work with pagination (as i understand it is very difficult if not impossible for proper pagination to work on posts that are listed on a page).