No, the dry yeast was brought in by someone else. (But there's no problem using a stir plate with dry yeast, though I think you should give it a few hours before starting the stirrer. Or at the very least let it sit quiet in there for half an hour. Fermentis has found that vigorous stirring right after pitching the dry yeast directly to the wort, is bad. Just to have said that, I mean.)OK. Please realize my OP wasn't asking about dry yeast(s). I'm asking about stepping up liquid yeast and reaching a point where too much oxygen is bad (if this is a cause for concern).
As far as my knowledge goes the best practice is to avoid letting the starter spin after the yeast has consumed all the sugars. I'm not at all sure how much it will hurt the yeast if it is fed oxygen after that has occurred, and I don't understand the biochemistry of what then happens. The yeast will go on feeding on the ethanol - that much I know - so the premise is that that is bad. But I'd dearly like to know why. The hurt presumably is that the yeast depletes it's energy stores, and it needs those stores to build sterols and fatty acids, using oxygen, when you pitch it to a new wort. That process is critical to a healthy fermentation, so you want to pitch yeast with good energy stores.
Of that last point I'm fairly certain, at least. But I'm not sure you need to worry much if your starter has been spinning a bit too long. I'm not sure you don't need to, either.