I agree with Jeff Morrow and upvoted him. But let me add some thoughts.
Yes, there is nothing wrong, grammatically, with comparing a single thing to multiple things. To simplify his example, it would be completely correct and not strike anyone as strange to say, "President Biden is like other presidents because he also ..." (Whether the comparison is positive or negative. Not here to debate politics, just discuss grammar.)
It would be completely normal to say, "This chair is like those sofas you were complaining about yesterday. It, too, is poorly made and low quality."
What makes your examples ... awkward ... is that we don't normally compare people to furniture, except as a joke. If you said, singular or plural, "These cabinets are like the guy from yesterday", or, "This cabinet is like the guy from yesterday", I'd think you either mis-stated what you were trying to say, or I would be waiting for the punch line of the joke. When I first read your example I thought it was a mistake, you meant to say, "These cabinets are like the cabinet the guy was looking at yesterday", or "The guy looking at these cabinets today is like that other guy who was here yesterday looking at cabinets." Not because there's something wrong with comparing a singular to a plural, but because it's odd to compare a piece of furniture to a person.
Not wrong or impossible, just odd. We do sometimes compare very unlike things. Like Shakespeare's poem, "Shall I compare thee to a summer's day?" It's a strange comparison, but then he goes on to explain it so we understand.
Just by the way, the example about mystery doors doesn't really make sense. It's not grammatically wrong, but logically wrong. "They're not mystery doors? She doesn't exist either." But if they're not mystery doors, that implies that they are something else. That is, they do exist. They exist, they're just not mystery doors. I think what you meant is something more like, "My girlfriend is like the hidden door by the fireplace. There is no hidden door by the fire place? Yeah, my girlfriend doesn't exist either." Of course a joke doesn't have to make logical sense, but I think this doesn't make sense in the wrong way.