Can a pitcher blow multiple saves in the same game?

I know the intuitive answer is no, because once a pitcher enters the game in a save situation and blows their team's lead, that save opportunity has been spoiled, even if their team later retakes the lead.

But what happens if the pitcher changes positions after blowing a save, their team regains a narrow lead, then the same player switches back to pitcher? If any other player took the mound in this situation, it would be considered a save opportunity for them. Would this also count as a save opportunity for the player retaking the mound? If it would, then wouldn't this imply that the player could proceed to blow another save (or potentially earn a save)?

The MLB Glossary says that the player must "enter the game" amid save circumstances to be eligible for the save, but we have to interpret this as the player entering as pitcher, or else Steve Wilkerson wouldn't have earned a save for his July 25, 2019, game in which he was the Orioles' starting outfielder. It's not obvious whether a player who pitches, plays another position, then resumes pitching has "entered the game" multiple times for the sake of this definition.

Wikipedia says, "A reliever cannot blow multiple saves in a game unless he has multiple save opportunities, a situation only possible if the reliever temporarily switches to another defensive position, then returns to pitching." However, this is uncited, and I can't seem to find official sources that corroborate it.

There was some discussion about this topic in this Baseball Reference thread, but it was inconclusive.

The question has come up in this subreddit before too, but it didn't seem like there was an authoritative answer.

I'm hoping a stats wiz here can answer this confidently and correctly. The question has split my own family members when I've asked them about it!