I think that it is really negotiable. You need to check with lawyers regarding ROFR, but overall I wouldn't see a problem if you told all your existing investors if you would like to substitute one investor for another during the search phase. I would be a bit surprised if any of the traditional SF investors would insist on ROFR provision during the search phase.

Also, you don't really need to do this now - you can (and I believe should) keep contact with some investors outside of your cap table so that you have access to equity gap capital if it is needed when acquisition happens.

PS Just my perspective as a fellow searcher - to get a good perspective of an investor, if I were you I'd speak with someone on your cap table who is a traditional SF investor and whom you really trust.

Tagging a few traditional Searchers & investors that have recently completed transactions that might be able to share their perspective:

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In my view it is not very fortunate, but keep in mind that investors in a search fund don't automatically invest in your target. Even if they would have disposable income, they could still opt out from participating in the target acquisition.

Hi. It's important, in my opinion, to understand his/her plans. Having the right but not the obligation to invest on a potential acquisition, gives you not much flexibility to act, since the investor could be happy to get its 150% of what invested as shares, creating a potential small equity gap for you. In that case, he would be extremely diluted, so not that interesting for him/her and more convenient to sell unit now.

If you find a good transaction that has an equity gap from one investor dropping out, it shouldn't be terribly hard to find someone to plug the gap - if anything the process is already slightly derisked. You could start talking to some prospective equity gap investors now and keep them up to date on your search so that when the time comes they will feel more comfortable with you and your team.

Yeah unfortunately not alot you can do here, barring some flexibility in your legal docs. In reality that person is probably not the only investor who will not bring follow on when you look to fund your deal. Each investor has a slightly different style and pain points so it's very tough to find something that every investor wants to follow through on. Usually if you have a good enough deal, other investors in your fund will pick up the slack or you can reach out to others In the community to pick up the rest.