Can a wee plane have different engines ?

Been talking with a work colleague this weekend who tells me he witnessed a “British Airways plane” on finals to 023 at Glasgow through the week there,

He knows nothing about aircraft but it was low and he is convinced it had two engines that were differing greatly in size. By his description I make it to be either a BA 737, A320 or 757 at the most.

Is it possible that such an aircraft would operate with let’s say a Rolls Royce and CFM pairing ? Would it be a testbed ? Why would a short hauler have different engines on board ?

He is very certain that the starboard engine was noteably larger than the port side which he described as being “long and narrow” making me think of the A320 and it’s CFM turbofan.

Any ideas folks ?