Will higher end objectives from Zeiss, Leica or Olympus thread into an Omax microscope?
And will they resolve images better than the objectives that come with an Omax or one can buy from Omax?
Probably, yet there are several conditions for successful replacement:
1. That the objectives are of the same type of correction. Infinity corrected objectives do not fit on a fixed tube length microscope (160mm, 170mm) and vice versa.
2. That the parfocality length is OK. For example, short barrel (yet excellent optically) objectives (example: early Olympus objectives) might be two short for focusing on a microscope that accepts DIN optics.
3. That the objectives have the same thread as the nosepiece. This has been true for many objectives but modern objectives from the major brands can have a different thread, namely, not RMS.
Features 1-3 are part of the known specs of the objective in question.
4. That the objectives (if they are finite tube length) match the eyepieces with regard to corrections/compensations of aberrations.
This might be known from the experience of other microscopists.
5. And if those conditions are fulfilled, there are still surprizes. Theoretically, resolution depends on the NA of the objective, but in practice, the contrast afforded by the objective also matters. A prime-make objective might be superior than an inexpensive one in one respect, and inferior in another respect. Unless, perhaps, the high-end objective is the top of the line (and most expensive). See, for example, the two-part very comprehensive comparison, published on the web by Robert Otoole back in 2017. I forgot the link, but it is there somewhere. He compared AmScope to LOMO to Nikon 4X objectives.