Self Funded Search: Handling Partner Dilution

In a self funded search partnership, where three partners are contributing all the equity (no external investors), what's considered "market" for handling dilution when one partner out of three can't contribute capital pro-rata with the other partners in a follow-on equity round? How have other search partnerships agreed to value the business and calculate dilution for these subsequent contributions? Additional context: We have a three person partnership doing self-funded search. Two founding partners have more capital, and are willing to invest a larger amount, than the third partner (me). We're each willing to invest $400k a piece, for a total of $1.2 million of equity. This may turn out to be more than enough to cover the initial acquisition, post-close liquidity, and tuck-ins, especially since we will be leveraging SBA debt, and plan to use debt to finance tuck-ins, to the extent possible. We plan to invest equal amounts, pro rata. However, in the event that we need more equity capital in the future than the $1.2 million, the two founding partners want to have the right to invest beyond their $400k amounts, and not have to raise capital externally. The third partner would prefer equity to be raised externally beyond the $1.2 million, and would want to be protected from being excessively diluted by the other partners if he can't match their investments. How is this typically handled in operating agreements? If two of the three partners wish to invest additional equity, and the third partner can't or doesn't want to match, how is the valuation of the platform set to determine dilution, if there is no external party to set a clearing price? I know there is preferred equity and mezz available out there, which is much less dilutive than common equity, so I'm trying to incorporate that into the thinking as well. Looking for approaches that protect the capital-constrained partner while fairly compensating those contributing additional capital. Would really appreciate any thoughts folks have here, or if anyone is willing to share operating agreement language around this. Thanks in advance.