Bit of a noob here but I recently discovered Tampermonkey and it's amazing ability to use js userscripts on webpages. But since it's only found as a browser extension and I use multiple browsers, I was wondering whether there would be a sort of system-wide (Windows 10 btw) alternative to Tampermonkey that's able to work with all or most browsers, just for convenience's sake. 

It'll certainly help with working with multiple userscripts instead of having to be on top of them for every single browser.