The Persona franchise has grown in popularity in the west, which has led to Atlus & Sega cross-promoting the series with other video games. One direct example of this is Catherine: Full Body, which takes place in the same world as Persona 3 and is part of the larger Persona universe as a result.
Catherine: Full Body is full of references to Persona, such as songs from the games appearing on the jukebox in the Stray Sheep, and plushies of characters like Morgana from Persona 5 sitting on the bar. These are meant to be moments of fanservice for Atlus fans, as many of them first encountered the world of Catherine in a Persona game.
There were multiple versions of Persona 3 released over its lifespan, with the last one being Persona 3 Portable for the PSP. It was possible to encounter Vincent Brooks (the protagonist of Catherine) in Club Escapade in Persona 3 Portable. Vincent gave hints about the strange things going on in his life, before reassuring the player that it had nothing to do with their story. Persona 3 Portable was released in 2009 in Japan, while the original Catherine wasn't released until 2011. This bizarre encounter with Vincent left fans wondering what Atlus had in store for this new character.
The release of Catherine: Full Body on PlayStation 4 in 2019 led to even more Persona references, as Persona 5 had been released in the years since the original Catherine. It was possible to play as Joker from Persona 5 in the DLC for the game, which included cameos from the other members of the Phantom Thieves. This took place in the Babel mode, which is set outside of the main story for the game, so Joker's encounter with the nightmare world is considered to be non-canonical.
Persona 3, Persona 4, and Persona 5 all share the same setting, due to references made in each game. The main characters of Persona 4 visit Gekkoukan High School during the events of the story, which is the main setting of Persona 3. The cast of Persona 4 is referenced in Persona 5, as Goro Akechi is described as being the second coming of the Detective Prince, with Naoto Shirogane (one of the party members in Persona 4), being the first. The timeline isn't exact, but it's clear the later Persona games take place in the same world, but at different times. There are some direct crossovers between the games that have happened, like the battle against Yu from Persona 4 in Persona 5 Royal or the events of the Persona Q games on the Nintendo 3DS, but these take place outside of the boundaries of continuity.
If Vincent exists in the world of Persona 3 Portable, then he also exists in the world of Persona 4 and Persona 5. He has to deal with his own supernatural enemies, but these are unconnected to the events of the Persona games. There are thirteen endings in Catherine: Full Body, so Vincent's fate following the events of his game is ambiguous. It's possible he is still alive during the events of Persona 5, or he may have perished along the way. Players might never know the answer, barring a cameo in a future Persona game or a sequel to Catherine in the future.
Catherine: Full Body is available now for PlayStation 4 and will be released for Nintendo Switch on July 7, 2020.