Can I negotiate faster vesting later while I am working for the company?
Probably not. If a company makes a grant with a specific vesting schedule and the schedule is later shortened from its original terms, the accountants will usually make the company take a charge to earnings for the incremental costs either at the time of the modification or when the event occurs to accelerate the vesting. At the time of your grant, whether of options or restricted stock, you can suggest accelerated vesting based on performance goals, with the grants still vesting after a set term. This would avoid accounting complexities for your company.
In some situations, you may be able to negotiate accelerated vesting as part of a severance agreement.
Alert: Check your stock plan and grant agreement, as it may already have provisions that accelerate vesting for specific life events (e.g. death, disability, retirement) and/or a change in control at your company.