I wish there were some way to rebrand as (as peculiar as this is in America) KJR-1, KJR-2, KJR-3, etc.
I know that Canada will allow AM's and FM's to employ boosters that will copy the main callsign in the way that you suggest, and the repeaters can be on any frequency they wish, whether that would be the same channel, or on a different one entirely. So you have CKRY on 105.1, and CKRY-FM-2 on 93.9, or you have national networks like the CBC and the ICI (or CBC's French arm of broadcasting). It would be possible, then, that a Canadian KJR could be CJR in 950 CJR-2 on 1090, CJR-FM-1 on 93.3, and possibly CJR-FM-2 on 95.7. On top of that, you also can apply for an auxiliary signal on the same frequency (a nested signal, as it's called up there), to place closer to downtown to help service that area. And some stations have up to 10 rebroadcasters!
In the United States, the practical equivalent of this is applying for FM-boosters, however, we are stricter about this because you have to make them a certain percentage of the original power, and they must be within the FCC defined 60 dbu contour of the primary station. Also, all boosters must be on channel, or it's called a translator, and translators get their own callsigns.
However, you could still theoretically brandish a station however you would like. For example, you would mention the callsign at the top-of-the-hour as normal, but the rest of the time, you could refer to the station is KJR-AM2, KJR-FM3, 2KJR-FM, or any other combo you can think of, as it is practically the same as calling your station 95.7 The Jet, or Froggy, or Kool, or Kiss, or Hot, etc. as so long as your TOTH (top-of-the-hour-id) is the legal callsign that the FCC gave you.
With those rules in mind, imagine this stop-set: "We'll be right back to Seattle Kraken hockey on KJR-3, but first our legal id: KJR Seattle, KJR-FM and HD1 Seattle, KJEB-HD2 Seattle. And now a word from our KJR-3 sponsors". We can see here that the official call-signs have been read aloud legally and clearly, however, the station refers to itself as KJR-3. Completely legal to do, and I'm surprised people don't do this anyways. Also, of course, EMF has WPLJ, WCKL, KKLQ, and KLVP, plus hundreds of stations coast to coast, but everyone calls it K-Love. That's how you game the system right there.