I'm a PhD student in social science, currently preparing for grant or fellowship applications with two PIs. Specifically, I'll apply for a postdoctoral fellowship with PI #1 and co-write a research grant with PI #2.
As there is no guarantee that I would be able to win the fellowship or grant, I'm working on this with two different PIs (Neither of them currently have a funding to support a postdoc. It's been only a week since I started communicating with each of them, so they don't know yet that I'll be working on two different proposals).
I'm going to suggest research ideas to PI #1, and suggests different, but pretty similar ideas to PI #2 (Let's call them Proposal #1 and Proposal #2). The thing is that I would like to pursue research ideas in BOTH proposals in the future even if I end up with only one PI.
There's an overlapping research question between Proposal #1 and #2. If I pursue this question with one of the PIs, would the other PI be upset about it? I'm concerned that the other PI might think that s/he contributed to the development of the idea (which hasn't happened yet, but likely to happen as we elaborate my initial idea for application).
Suppose the Proposal #1 is accepted, while Proposal #2 is rejected, and I end up working with PI #1. In this case, is it still okay for me to pursue or study research ideas from Proposal #2 without having PI #2 involved? Or should I bring PI #2 as a collaborator? If I must bring PI#2 to pursue research ideas from Proposal #2, I feel like I need to be cautious about which ideas to present to each PI because I don't want my research ideas to be bound to a specific PI.
Any suggestions or advice would be appreciated!