It sounds like you have may multiple hypotheses to test, not only if the experimental treatment is better than the 3 standard of care (SOC) arms, but perhaps if one of the 3 SOC arms is better than the others, at least for the profile of patients in the study?
You had indicated in your initial post, that you expect a reduction in delirium from 60% at baseline to 40% post treatment in the experimental arm. What reduction, if any, from the 60% do you expect in the 3 SOC arms?
In order to formally compare the 3 SOC arms against each other, you would need to define a minimum clinical difference that you wish to be able to detect and test for, in order to have a large enough sample size, and therefore power, to formally test that hypothesis at a pre-defined alpha.
If the difference across the 3 SOC arms is relatively small clinically, as compared to the difference in the experimental arm, that may not be something that you can formally test from a practical standpoint, because it will materially inflate your required sample size for the study, increasing costs, risks, and other factors. Thus, you may only be able to assess those differences on an exploratory basis.
You should have access to historical data that can give you some insights into whether or not that comparison is reasonable from a study design perspective, and what clinical parameters would be relevant in deciding how to treat a patient in the absence of the experimental treatment, presuming that the experimental treatment is ultimately better. That information should be reasonably well established for the SOC treatments.
A first step for you is to explicitly define, a priori, what hypotheses you wish to formally test, and what the explicit assumptions are for the differences in outcomes across the 4 arms. Once you can do that, you can better begin to assess the study design, and how to go about determining what sample size(s) you may need.
You may also have to determine a primary hypothesis, for which you formally power the study, and perhaps one or more secondary hypotheses, for which the study is not formally powered.
If you have access to local statistical expertise, that may be a better approach for you, rather than going back and forth here, as you can work interactively and more productively through the details of the study design process.