Re-aiming an established page at a new keyword trades the rankings it already earns; it doesn’t add the new term on top of the old ones. The page holds positions for the terms it was built around, and re-optimizing tells Google its context has changed, which can move it toward the new keyword while pulling it away from what it currently ranks for. The reflex to just drop the new keyword in ignores that the page already holds something, and the re-aim puts that standing at risk for an uncertain shot at the new target.
What decides whether the trade pays off is intent. If the new keyword shares the page’s existing intent, a phrasing variant or a closely related search the page already half-answers, then re-aiming mostly sharpens what was there and the downside is small. If the new keyword pulls against the existing intent, the kind of search that wants a different sort of page entirely, then you are asking one page to serve two purposes, and it tends to do neither well; you can lose the old rankings and still not win the new one. Treat the movement as observed volatility rather than a guarantee in either direction, because Google isn’t penalizing the change, it is re-reading what the page is now about.
So the question before re-optimizing isn’t which new term you want. It is what this page already earns, and whether the new keyword is close enough to keep it. Check which queries the page currently ranks for, weigh that standing against the new target, and re-aim only when the new keyword sits inside the same intent, instead of overwriting a page that is already working.