The biggest thing in terms of tax benefits is understanding where you fall on the Qualified Small Business Stock exemption (Section 1502 of the tax code).
If you sell shares after the 5 year mark, they could be tax free and Alternative Minimum Tax(AMT) free at the federal level. It's worth paying attention to that when setting your close date. There are some ways that you can extend the date of the secondary so that it crosses the 5 year mark, depending on how much time you need.
If there's no chance of doing that, there is also Section 1045, which allows for a "section 1045 rollover." This allows you to roll the investment into another QSBS investment and keep the clock ticking. It's obviously risky because you could lose it all in a bad investment, but a good taxlawyer can sometimes use that strategy to create a delayed exit.
Finally, rounds where there is a lot of demand can be a good time to split some of your ownership into a non-grantor irrevocable trust if you have/will have people you'd want to be the recipient (for example, i have kids). The value here is that QSBS only covers the first $10M in gains.. but that's per tax paying entity. So, you can gift shares to the trust at their current low value, thus using less of your lifetime gift exemption, and then get $20M in QSBS tax free coverage when the shares exit down the road.
Unfortunately, if you're in a state that doesn't federalize their tax law (such as California) the QSBS doesn't apply at the state level so you still get hit with California's 13.3% tax rate and state AMT. But, if you live in a state that does federalize (or has 0 personal income tax) the gains are completely tax free. Texas is the best state for people leaving California for tax reasons, because Texas will (apparently) argue on your behalf.
So, taking all of this into account, some people I know have created irrevocable non-grantor trusts based in other states, gifted the shares to that trust, and then sold the secondary that way.
It all depends on how much you want to mess around. Ideally the simplest case is that you have QSBS qualified stock, you're selling less than $10M worth, and you happen to live outside California or NYC. Everything else requires a good lawyer and a willing lead investor.
That's a summation of what I know. There are other good articles about QSBS, such as this one from Brown Advisory. Google will help, and your legal team should be well versed in this. I was surprised to find out how few people know about Section 1502 and 1045, so happy to share.
Step 1. Look at your issue date for your stock in the company.
Step 2. If it's less than 3 months away, talk to your lawyers about a delayed close.
Step 3. Profit!