Accelerating vesting of early-exercised stock?

[beiser]

Imagine that an employee at a startup is granted a number of ISOs, which are early-exercised with an 83(b).

A few years later, with those partially vested, and the fair market value of the shares substantially higher, he comes to a shared agreement with the CEO of the company to increase his stock compensation.

Is it possible to increase the rate at which the fully-exercised stock grant is vested, or would there need to be an additional grant issued at a different price to run concurrently?

It's unclear to me how the early exercise would interact with 424(h)3c—were the ISOs here "options not immediately exercisable in full"? 

[Linda Wilkins]

Beiser, the options were exercised in exchange for restricted stock subject to Code section 83(b). The options weren't "modified" before exercise so I don't see any impact of 424(h).  If the executive is to obtain additional stock compensation, rather than grant more early exercisable options (with a new FMV exercise price), I'd recommend granting new shares of restricted stock (although the 83(b) election may be cost prohibitive).

Your idea to accelerated vest the existing restricted shares (or improve the vesting schedule) is feasible although it wouldn't increase the overall equity compensation for the executive.