I am in the process of contacting potential supervisors for a post-doctoral position. I discussed my initial idea with 2 potential supervisors, but now I refined the idea and I found 2 more supervisors that fit within the scope of the project and that are interested in searching for funding together. The ideas are linked together, so my question is should I apply for funding with 4 supervisors? When is it expected to include someone into a grant proposal? At the moment nothing is written or decided, I was only proposing ideas. I am just feeling naive on these poitics matters. In my head, the best would be to have a first postdoc with 2 supervisors and a second postdoc position with the other 2 that seem interested.
There are oh-so-many things to govern this decision.
First, a post-doc should be about you establishing your own vein of research and experience in handling a grant. With too many "superiors" involved, you may end up doing little more than answering to them, as a graduate student does. This is not a dissertation committee, it should be a working group of peers that launch your career. From your comment it sounds like there is heavy redundancy in your 'team.' If you are doing an ecological experiment with X population for A behavior and B technique -- which thing is your expertise? It sounds like your working group could 'work' entirely without you. That's not good.
There are two ways you can approach this.
Only have supervisors who are more senior experts in your exact area of interest, thus ensuring you get the pedigree of an area expert through this project.
Only have supervisors who are not in your area of interest so that you are the area expert. For example, if you are the behaviorist and are trying to establish yourself in your field as such, don't answer to other behaviorists, only methodologists. Be your own boss.
Choose between strategies 1 and 2 based on your long-term career goals.
There are other, minor considerations: you need to carry at least one person who has a solid track record of competently handling scientific funding to be co-investigator. Also, if you do not have a few publications in the area, you better include someone who does on your grant proposal. It would be ideal if the funded/published is the same person.
Finally, don't burn bridges. You can always publish with someone later.
Four supervisors seems like a lot, and could potentially put you in a situation where you either fall through the cracks ("she has three other advisors; they can deal with this") or get pulled in multiple directions.
Three pre-arranged collaborators, however seems great! Think about the project after this one. What would you want to do? How would you write your first grant as a totally independent PI?
Perhaps you're interested in methodology. "The Anna Lab is interested in understanding how animals spend their day. As a postdoc, I developed a technique for tracking the sleep-wake cycles of wild lynx. We develop activity trackers to learn what fish, birds, and squirrels do when left alone in their natural habitat."
Maybe you're interested in the behavior itself. "Sleep plays an important part in animals' daily routines. The Anna Lab compares sleeping across species. Do related species share common sleep habits across habitats, or is the sleep-wake cycle regulated by environmental cues?"
Finally, perhaps you're fascinated by the animal or site itself. "Little is known about the solitary lynx, one of the most reclusive cats"
Hopefully, one of these sounds like you. Choose that person as your primary supervisor (assuming you like them well enough personally, etc.) and then set up strong collaborations with the others. This will ensure you get strong training in whatever you're most interested in, while allowing you to impress others with that skill too.
Congratulations on finding such a good fit for your interests!