If I write an unsuccessful grant proposal with one PI, can I reuse those ideas on a different proposal with a different PI? I'm a PhD student in social science, currently preparing for grant or fellowship applications with two Principal Investigators (PIs, formally in charge of the project if the grant proposal is successful). 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!
Generally speaking, it is fine to seek multiple sources of funding for the same project.  However, you cannot accept multiple sources of funding to do the exact same thing without permission.
You should check with the program managers of the funding agencies.   Program
managers say they spend much of their time looking for duplicate submissions and rejecting them.  However, if one application is to a government agency and another application is to a private foundation, that might be fine.  Or if the applications are to governments of different countries, that might also be fine.
The PIs should understand that it is normal to seek multiple sources of funding.  But tell them what you are doing and ask them if they are okay with it.