To understand the dilemma at hand, one must first understand the psychology behind the constituent parts - psychosis, psychoactive and anti-psychotic drugs. For this, we utilise the key notion of the unconscious.
I can say from a matter of experience that psychosis relates strongly to the unconscious. In fact, to generalise from my own experiences I could say that a psychotic episode coincides with an encounter with the unconscious which goes deeper than one has had significant access to in the past. It is a matter of charting new territory. Now, one may run into difficulties while having such an experience, and when these difficulties become pronounced, it is then that the term "psychosis" is used, although the term applies even if, at least to the individual undergoing the experience, there is no noteworthy trouble. However, it is a common axiom (albeit unexpressed quite so explicitly) that the unconscious is a dangerous place to be avoided, and hence requires treatment. While there are dangers to being overcome with the unconscious, that is by no means the rule, and instead points to a bias common to those who have yet to experience their own unconscious, or have an agenda to keep people out of touch with their unconscious. It may or may not be that while diving into the depths of one psyche, one needs to be brought back to the surface immediately, and hence anti-psychotics are administered as treatment.
So, logically, what do anti-psychotics do? They remove a great deal of your contact with your unconscious. They put a barrier between you and the harder to reach places in your mind. (Alcohol also makes it harder to access the unconscious, but the mechanism seems to be of a different kind entirely, for instance the removal of inhibitions in the drunken state compared to the heightened inhibition and fatigue in the state induced by anti-psychotics). So, due to it being harder to access, the unconscious becomes less apparent. The unconscious is still active, however the individual, who could have benefited from knowledge of what was taking place, now finds themself in a rather barren landscape.
And what do psychoactive drugs do? Hallucinogens, and to a lesser degree cannabis, have the effect of activating the unconscious so that one becomes aware of it. So, they act in a contrary manner to anti-psychotics, and induce a state similar to psychosis. The difference is that, whereas during psychosis one is exploring the next frontier of the unconscious, with hallucinogens, certain unconscious "zones" are predictably awakened (whether one has reached, passed, or not yet reached that particular zone). Cannabis activates a zone which is more unconscious than even your 8th cognitive function, and mushrooms and LSD activate a zone more unconscious than that (and DMT activates a zone even more unconscious than that).
So what you'll find is that being in a psychedelic drug trip is quite similar to being in a psychotic episode, while the anti-psychotics will make it more difficult to fully immerse yourself in the trip.
So now we can analyse the question.
Whereas for myself, I've found psychosis to be a primarily positive experience, you the reader may have not found that to be the case. So there may therefore be reason to expect that you would have a bad trip if you were to use hallucinogens, because you perhaps have negative forces within your unconscious mind that you have not dealt with.
Also, while it may seem like a good idea to "double the dosage" in order to "bypass the anti-psychotics" I can speak from personal experience against this idea:
While not hallucinogens per se, I have in the past used synthetic pot (a freakish class of drugs which I do not recommend). Most of that use was while I wasn't on anti-psychotics, and I found it to be a weird but enjoyable drug (one, however, which ultimately seemed to wreak much havoc on my life). I did however use a bit while I was on anti-psychotics. What I first noticed was that the effects weren't as pronounced as I remembered. So I ended up using more of the drug than I otherwise would have - I used an amount that I would have used if I had a strong tolerance, but at that time I did not have a built up tolerance to it (it had been around a year since the last usage). Eventually while using it my mind kinda "snapped" and I found myself spiraling into a psychotic episode - the scary kind. So, rather than being a protective mechanism, the anti-psychotics seemed to have interacted with the drug in a way which had disastrous consequences. The few weeks that followed that drug use were awful, and it took several months before I can say I had really returned to normal. Now, synthetic pot is particular nefarious in its effects, known for causing all sorts of strange and horrible side effects, but I believe the same principle applies here, because of the overlap regarding activation of the unconscious. The drug may interact with the anti-psychotic to produce bad side effects and doubling the dosage won't create a usual trip but rather you will be unaware of the so-called tidal wave it can produce. I don't think the idea of mixing a psychoactive drug with an anti-psychotic drug is entirely unwarranted, because I've heard that one of the main chemicals in cannabis is an anti-psychotic, but the idea of doubling the dose to bypass it could end disastrously.
Now, regarding unconscious - if you experience negative influxes of unconscious attitude, I would suggest starting with some self analysis. What is it about psychosis that you don't like? Why don't you like it? What do you like about it and why? What are your reasons for wanting to explore your unconscious further (i.e. use hallucinogens) given what you've experienced? First start with establishing good rapport with your unconscious without the use of drugs before considering adding them into the mix.
Important: if you're going to use hallucinogens, and this probably goes for many drugs, make sure you're in a) a good state of mind, and b) a good environment, preferrably with c) a trusted friend who is not using drugs. You want to be in a state of mind free of anxiety, in an environment where you feel safe, with a mindset of enthusiasm (or perhaps more aptly, wonder) for making contact with your unconscious in such a manner. You'll want someone trusted close by in case anything goes wrong. Even with the proper precautions, a bad trip can emerge, and having someone there to help keep you safe and grounded will be of great benefit (though if you don't trust the person, they could themselves become the source of a bad trip).
Lastly, I'll make mention of the fact that the mind is a very powerful thing. While you may desire contact with the deep-space psychic zones of the psyche, you can make contact with these without drugs. One simple but potentially effective mechanism is simply to pretend that you're doing drugs, but all sorts of things like meditation, or anything which heightens psychosis in a positive or neutral sense could do the trick. I would strongly recommend attempting to make contact with your unconscious in whatever natural means you can before trying artificial means. Yes, this is more difficult if you're on anti-psychotics, but a quick-fix jump off the diving board and subsequent plunge into the depths is perhaps not the first line of action I'd be taking...
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Source: look up "8 circuits of consciousness" for brief descriptions of what I've here closely referred to as "zones", and links to different drugs, psychosis etc.