I'm afraid you can't. You need to add the new inks (supposing thay you've managed to overcome the coded chip system), which will then mingle with the ink in the internal reservoirs. It can then potentially take a very long time to flush out, since there will be mixing in the tank and the proportion of old ink will drop exponentially slowly (ie there will always be some left). So it would be best if the new and old inks ere essentially the same in colour.
Note that some are of the belief that some of the colours have no adequate 3rd party replacements.
Otherwise, you could tell the printer that you are going to move it, and let it empty the tanks into a couple of aste tanks. I'm not sure how complete a job it will do.
Personally, I wouldn't do it: mostly the 3rd party inks have much lower endurance, most have at least subtle colour differences, the chip system is a pita.