Latuda is a tricky one, with it being an atypical antipsychotic there aren't any easy drugs to compare it to. Also part of what is going to effect things is what you're taking it for. For example, I have a family history of schizophrenia and I know that all of the drugs you mentioned tend to make those symptoms worse. So if you're taking it for that then it may be best to refrain from taking any psychedelics. However when it comes to bipolar disorder that is usually much less of an issue. So if you're taking it for that then you may be fine. There's a lot of variables at play.

Just looking arroud, for most people, it looks like Latuda kills all the effects of weed, shrooms, and DMT but LSD still works normally. So far I haven't seen any reports of severe negative reactions with any of those but with this being a more uncommon drug that doesn't necissarily mean much.

Honestly try just talking to your psychiatrist. They know your exact situation with your diagnosis and med list. A good psychiatrist should be focused on harm reduction and not judgment. Most psychiatrists know their patients do other drugs anyways and would actually just prefer to know which ones so they can help them do so safely and so that they know not to put their patient on a med that has major interactions with those drugs. If you tell them and they're at all good at their job then odds are they will tell you that taking any drugs with your medication is a bad idea, because they're practically required to say that. But then they should be able to tell you how to do your drug of choice safely. Just recently I spoke with my psychiatrist about going off of one of my meds because I wanted to be able to do shrooms again and they were super helpful. They took me off that med and pointed out that another med I'm on would also interact with shrooms but I could just not take that med on any day I planned to do shrooms. But of course you are going to know your psychiatrist better than any of us so if your psychiatrist is not that kind of person then you may just be stuck rummaging around the internet for scraps of info.