Is it possible to re-engine aircraft with different engine options?
It's doable, but not easy. Unless the aircraft was designed with that in mind, even then it does pose challenges. An example would be the Boeing 787:

The two different engine models compatible with the 787 use a standard electrical interface to allow an aircraft to be fitted with either Rolls-Royce Trent 1000 or General Electric GEnx engines. This interchangeability aims to save time and cost when changing engine types; while previous aircraft could exchange engines for those of a different manufacturer, the high cost and time required made it rare.

The benefit of interchangeability makes leasing aircraft easier for the lessor, as their fleet would be compatible with all the airlines and their existing facilities.

[Once] a plane has one type of jet engine under its wings, it’ll always have that type of engine. It’s just too time-consuming and expensive to swap out a Rolls-Royce in favor of a new General Electric.
This complicated the sale and leasing of jets. If Airline A wants to lease a plane from Airline B, but the two didn’t use the same kinds of engines, that usually would sink the deal (Source).


Related and further reading:

How much would it cost for a large airline to switch engine manufacturer for their planes?
Why bother having different engine options on one aircraft?
Boeing still hasn’t solved engine swap ‘challenges’, 2007