Can I Mix Ink Cartridges Of Different Manufacturers?

The printer will report no trouble at all, and I don't think you'll notice any difference. What will potentially happen when you mix ink from different manufacturers is that color reproduction will be wrong, because the different manufacturers tune their inks slightly differently. I do not think the effect will be noticeable, though, in anything less than a professional imaging environment.

You should not have any issues printing in general. Keep in mind that the quality of the ink cartridge from brand Y might not be aa good as OEM; whether or not that is an issue is up to you.

Depending on the manufacturer of the printer you might lose a key piece of functionality though: the ink cartridge may no longer report its fill level. Some printers will just keep telling you that you are out of ink but still allow you to print while others may stop printing altogether, as it reads brand Y as being empty. This happens with smart print cartridges that report levels back to the printer. It can read your full ink as empty because the counter on the printer did not reset.