Generally, a given browser ships with a single JavaScript engine. There is no need to ship with multiple engines, because if additional features are required of the engine, they'll simply be added to the engine which the browser ships with.
I could potentially see the existence of a modular web browser which requires plugging in a JS engine separate from the main program (which could then result in the user having multiple JS engines on their machine), but I know of no such browser, and thus know of no means by which JS could be used to swap the engine.
I suppose you could implement EMCAScript in JavaScript, but that seems like a tremendous hassle.
In response to the edits to your question: I believe Chrome Dev Tools' mobile emulation will get you what you want instead of what you've asked for.