I sometime stay at the Aloft River North on Clark street in Chicago. It shares valet parking with the Hyatt Place next door on Clark and the Fairfield Inn around the corner on Illinois. The first time I used the exercise room in the basement I was amazed how large the basement was relative to the hotel so I explored. It turns out all three hotels are part of one large building with different elevator bays but are connected at the basement level and on some of the floors. So you can literally enter the Aloft and exit around the corner at the Fairfield. Also one stay the Aloft was having elevator issues so they told you at check in how to cross over and use the Hyatt's elevators. When you look at the building form the outside the hotels look separate but they are just one large building.

2 different hotel chain brands sharing the same pool
 

Hilton Manila and Sheraton Manila share the same swimming pool, but other than that they have separate facilities; individual ballrooms, gyms, club lounges, separate lobby and entrance.

Built as a casino resort building with 390 rooms for Sheraton Manila and 357 rooms for Hilton Manila.

Accor has been having multiple brands on one site or in close proximity to each other for years in France. There are many sites in France with, for example, an Ibis and Novotel in separate buildings next door to each other. Recently I drove past a site with a full house of the three Ibis sub-brands, Ibis, Ibis Budget and Ibis Styles all together, with an even more budget Formula 1 just across the road.

JW Parq Vancouver and Douglas Autograph Collection - two sides of the Parq Vancouver complex - the Douglas often has JW branded towels.

Newly opened Kabukicho Tower near Shinjuku, Tokyo, has the Bellustar Hotel (Pan Pacific chain) and Groove Hotel just underneath it (part of the Park Royal chain)

In downtown Los Angeles, the JW Marriott and Ritz Carlton share a 54-story building. I think the Ritz occupies around 5 stories. There has been talk of adding a second tower to add more rooms to both hotels. I'm fairly sure it's all run by the same management.

I just spent two weeks at that property. Really zero distinction between the HGI and HWS. From the elevator lobby, turn right for the latter, left for the former. Nice place but ugh the traffic. Did not notice any separate wifi but maybe it was.

Springhill Suites and Residence Inn, 410 N. Dearborn St, Chicago

Marriott has done this for a while - one of their newest is a common building for a Fairfield Inn and a TownePlace Suites on Warm Springs Road in Las Vegas. I haven't been in to know if they do a common breakfast area.

Seen a few Courtyard/RI that share the same building in major cities.

Specifically stayed at the Courtyard Central Park before and it shares the same lobby space but with different elevators from the RI. Presumably same management company and targeting long term or family travelers (RI) vs. more business travelers (CY) from a booking standpoint. Amenities and everything else virtually all the same -- I've always picked the CY side purely due to better earnings and when traveling solo I don't need any of the things delivered under the RI brand standards.

I believe Austin has one of these too.

I think Hilton does the same thing as well combining HGI and Homewood Suites in some areas.

I've also stayed at the Hilton Garden Inn Charlotte Uptown which shares a parking facility with the Hampton Inn but nothing else AFAIK (no shared lobby at least during my stay and no other obvious shared amenities albeit it was a brief stay).

The other obvious one that comes to mind is Hyatt Ziva and Hyatt Zilara -- they often go together (e.g., Cancun) with some shared facilities between the two with obviously one being Adult only and the other being Adult + Kid friendly

Makkah
 

I believe the Abraj al-Beyt complex in Makkah, Saudi Arabia has a few hotels inside. For sure they have a Raffles, as I wandered around the lobby for a bit.

The Dorian, Autograph Collection, and the Courtyard Calgary Downtown - same building with the Dorian on top

Springhill Suites and Fairfield Inn in Moab, UT.