Well with Caesar still alive, I think that would make a stronger rivalry between him and Joseph to eventually push themselves even further. The fight with Kars could have also went differently as with Caesar's long range they might defeat Kars sooner, but I personally doubt that. So I think Joseph still loses his hand when he originally did, but he would likely be a lot stronger in part 3 if Caesar was alive, and I also would give Caesar a family and him and the rest of them would have a stand. Caesar's stand is probably another Hermit Purple like Joseph realistically, but I can see him having a grandson and granddaughter who tag along in Stardust Crusaders, but I think he would have a son who dies against Dio before Part 3 begins and he stabs himself Dio's arrow and that's how the Zeppeli's get there Stands. (And this would be the same arrow that is used to give Pucci and Weather Report there stands, plus the same arrow that Polnareff had in the final fight of Part 5 against Diavolo.)
There's many routes this could go in, because now Dio has 2 (maybe 4 depending if his grandkids are taught, which I'm still debating) hamon users he could take from, but now Dio also has more trouble. Thankfully, because of Dio's nature, he'd play around a bit which would lead to them discovering the ability of time stop differently. Iggy's death would not happen because Caesar would use his bubble cutters on Vanilla Ice which would accidentally reflect the sunlight onto him, which would reveal his weakness earlier. Avdol's death is unavoidable though, so unfortunately Avdol would still die to Cream. Caesar's kit is really useful against Dio, so before opening the coffin he may have the bubbles over it to reflect light just in case. If that doesn't happen, we could assume the teams would split differently, and I'll assume it's groups of four because that would be smarter(the smartest choice would be a whole squad but they're unlikely to take that option). In this case, the teams would be Caesar's grandson, Jotaro, Polnareff, and Iggy together, and Joseph, Caesar, Caesar's granddaughter, and Kakyoin together. Caesar would likely take the main fighting point because he has range that's greatly effective against Dio plus his hamon experience. Kakyoin would use the emerald splashes to deal with Dio, while Caesar and Joseph would likely support by keeping Kakyoin coated in Hermit Purple while also making it more difficult for Dio. Caesar's granddaughter (depending her Stand) would be helpful maybe but I'm not sure, that honestly depends on her Stand (I'm still thinking of stands for the grandchildren). Through this pressure, Dio would probably stop time before the 20 meter radius emerald splash takes place, but because all of them would be well guarded, he can't really do anything. This encounter would give enough time for Jotaro and the others to get here, and the fight would take place. If they play their cards right, the only stardust crusader (including Caesar and his grandchildren) that would die is Avdol, and in this what if, I will say they do play there cards right, Joseph, Jotaro, Caesar, Caesar's grandkids, Polnareff, Iggy, and Kakyoin would end up alive at the end.
Now as for part 4, Joseph and Caesar probably would not be in the state Joseph was in part 4, in fact they're more likely to look like they are in there early to mid 50's (While in part 3 they would probably look like they're in their late 30's/early 40's) because remember, if they both compete, their hamon knowledge and abilities would be better, meaning that the youthfulness could be greater. Part 4 would probably go on normally, and they could maybe locate Kira earlier because of Joseph's ability ACTUALLY being used, plus Caesar also having Hermit Purple. Would this save many people? Probably because I believe that Kakyoin and Caesar's grandchildren are also here too (when they show up, probably earlier then Joseph and Caesar honestly). He would use his range and emerald splash to the advantage, and might even pull out a 20 meter radius. This could prevent the death of Aya, plus Hayato 's dad, and the whole body change, and also Caesar's grandkids could show up here or maybe instead it's Polnareff who's here with Caesar's grandkids in Italy? IMO, Caesar's grandkids will be in DIU, while Polnareff is still in Italy, but Iggy would be with Polnareff IMO, so he's not completely alone. The part would likely be a lot shorter though, or maybe we can make a new main villain to replace Kira? But I think Kira would be defeated sooner (like Sheer Heart Attack arc soon), Aya would still be alive, and Hayato's dad is also alive that means. But unfortunately, I think that Shigechi would still encounter Kira and die to Killer Queen when he originally did IMO.
Part 5 would probably be Caesar and Joseph going to Italy with Koichi (his granddaughter I believe would marry Kakyoin after SDC, so she's busy with him, maybe the grandson shows up, but I don't believe he would). I could see Caesar would try assisting Giorno because Italy is his home, and Joseph would want to help his uncle. By the time they hear Polnareff's voice through recording, Caesar/Joseph is likely to try and call in the others who could try come in but I doubt it since Diavolo basically paid off everything to keep an eye on that kinda stuff, plus the final fight was happening in a couple of hours later, so unfortunately, no Jotaro, Kakyoin, and Caesar grandkids in Part 5, but I can see Koichi and Fugo maybe staying, but I'll think about it, and maybe even Abbacchio can survive? But I don't imagine to much changing, but I think that Caesar would die in this Part since I can't see him doing much against Diavolo but I can see him maybe dying in the place of one of the characters, and I can see Joseph being the one in the turtle in Polnareff's place because of the whole Joseph always cheats death thing. I also see Iggy in this part like I said earlier on, and like Caesar, I honestly believe that Iggy would die against Diavolo. IMO, I think Abbacchio and/or Narancia might survive, Bruno has a chance to live but it seems unlikely since I still think he goes through everything he originally went through in the part. But Giorno, Mista, Trish, Fugo, Koichi, and Polnareff are surviving Part 5, with Joseph being stuck in Coco Jumbo, Abbacchio and Narancia are 50/50, Bruno most likely still dies unless Caesar takes his place, but Caesar and Iggy I feel are dying to Diavolo regardless.
Part 6 is the first part that Caesar and Joseph are finally out of the story (this is because Caesar would die to Diavolo while Joseph is stuck in Coco Jumbo), but Caesar's grandkids, Kakyoin, and Polnareff (because now he is healed by Giorno after the Diavolo fight), would be in it. What would this do? Honestly, the part starts off the same, but I think Kakyoin and Caesar's granddaughter would have twins, one son and one daughter to actually join the story, with Jolyne and Kakyoin's son dating and being a couple somewhere in the story, with Anasui being jealous, and I see the daughter hanging out with Jolyne, Ermes, and Foo Fighters. I also think Caesar's grandson and Polnareff maybe have kids, Polnareff unlikely though, but I would like to include Josuke in the part, maybe also the other Morioh Warriors? I personally don't think Stone Ocean would start with any real changes but I will think of Stand's for the new characters . But Foo Fighters and Weather Report's deaths I think would still happen I believe, and I also think that Kakyoin, Caesar's grandkids, and Polnareff would return with Jotaro in the final fight. Now I think that with more characters here, this definitely makes the Pucci fight a lot more unpredictable. But I think that Anasui and Hermes could still die against Pucci when they originally did, unless someone takes there spot or maybe they have a healer or if Josuke is still around, maybe more characters die to Pucci, but I think that instead Kakyoin would use the 20 meter emerald splash to go after Pucci. This definitely would distract Pucci long enough for Jotaro to pull off one last time stop and actually put an end to Pucci before the universe could reset.
And after that, maybe I make more JoJo parts maybe?
But that's my story on What If Caesar Survived. I know this isn't good, but I think it could be something fun, like a fanfiction or something. Anything I can work on, tell me in the comments, as I'd like some criticism on my story. Tell me some opinions you guys have on this timeline, like regarding who should live and die?