There used to be an extension for Firefox called "IE Tab for Firefox" that used the IE rendering engine inside a Firefox tab, for sites that only worked in IE.

The same idea with built in Internet Explorer in Microsoft Edge, where you can switch to Internet Explorer mode and open website that only correctly works in Internet Exlorer

And Google made basically the opposite thing to embed Chrome within Internet Explorer for sites that wouldn't work in IE.

https://en.wikipedia.org/wiki/Google_Chrome_Frame

There are some browsers that support multiple rendering engines out of the box, like Maxthon (Blink + Trident) and Lunascape (Blink + Gecko + Trident).