Ask HN: Restructure during financing round

We have VCs interested in doing a round of investment in our company. My co-founder still holds on to a sizable chunk of equity, but in the last two years has become of less importance to the company. One of the stipulations for investment is a restructuring of the existing cap table to make sure the right people are incentivized going forward. Since my partner and I (the other two cofounders) have all of our worth tied up in the company, we have no means to buy out our third partners, so the restructure would have to take place via the VC deal. In theory, everyone participating in the deal is on board with this idea. In practicality, I'm having a hard time finding precedent. For anyone who has experience in M&A, what's the best way to accomplish this goal?