We would probably warn the customer that there will be some differences. Typically we would need to make some adjustments on press, like increasing pressure on some of the top colors that no longer have a base under it, just so they get onto the garment clean.
We would try to really plan it out in the seps if we knew that was happening. It would also depend on the artwork. If you are using Black shirts and if you are using a Black screen or not using a Black screen would all need to be considered. Or how your white base interacts with the shirt color, cranking up the seps on the white base would help like 1964GN said helps too. Or also if your top colors are blending with a Black shirt at all in spots would have to be considered.