[Digital-Citizen]

It's important not to lump together the proprietary browsers (where the limit you speak of can only be worked around if the proprietors allow) and free software browsers which respect your software freedom, like Firefox.

You could modify Firefox source code to let you run whatever add-on you wish. With Firefox whatever changes you want are limited only by your willingness to implement them (either by doing the work yourself or working with others to get those changes made).

You can even distribute the improved Firefox variant browser to others and help the community. Hacker News recently had a story about some hackers doing exactly this with a variant they call Librefox. Other examples of Firefox variants include IceCat and the Tor Browser.