Adding and removing keywords
You can change the set at any time. Keywords you keep hold their full history; the ones you remove take their measurements out of every average.
Open the market, edit its keywords, save. The change takes effect from the next capture.
What happens to history
Keywords you keep are untouched. Their history continues without a break.
Keywords you add start from zero. They have no past, so they contribute nothing to comparisons with earlier periods until they have been captured a few times. Expect coverage to dip briefly: the new terms count in the denominator immediately, and you are not ranking on them yet as far as the data is concerned.
Keywords you remove stop being captured, and their measurements leave the averages — including for past periods, because the averages are computed across whichever set is current. A chart can therefore change shape after an edit without anything having happened in the market.
That last point is worth sitting with. It is not a bug and it is not avoidable: an average over a set has to pick a set. If you want a before-and-after that stays comparable, change the keywords in one deliberate move rather than a few at a time.
The knock-on effect on competitors
The competitor set follows the keywords. Adding terms brings in whoever ranks on them; removing terms can drop competitors who only appeared there. If a rival you care about is not being tracked, the fix is to add the keywords they win on. See Which competitors you track.
The product itself cannot be changed
The ASIN a market was created with is fixed. To track a different product, create a new market — that keeps the two histories separate, which is what you want anyway.