Is it possible to manage third party web browsers with Group Policy?

I'm not sure if this is the right forum topic for this question but here goes. We are looking for a way to manage third party browsers such as Chrome and Firefox. We have traditionally only allowed our users to use IE 9 but have been forced to make Chrome and Firefox available due to some compatibility issues with IE and some of our newest cloud based applications. The issue is that we were able to manage most of the setting values for IE through GPOs in Group Policy but I don't know how we can manage the application settings for these third party web browsers. If someone has an answer to this dilemma, I would really appreciate it. Much obliged.

Good to see a fellow school network admin here. Not sure how big your system is. We use a solution called PolicyPak. We have a small staff and it allows us to make GPOs for nearly all of our primary third party user applications, including the two browsers you mention. It integrates with the Group Policy Management Console and allows you to create GPOs using the same basic GUI interface as the application you are creating it for. Doesn't require and real expertise to install it or any other hardware. We love it. Here is a link for how it manages Firefox. Pak for Firefox | Products

You will like this too, it has a trial mode and something called community mode which are both FREE so you can try it out as much as you want. Have a good one