It's not really "taxed" at the supplemental rate, they just "withhold" taxes at the supplemental rate.

Your employer has the option to withhold at the regular rate based on your W-4, or a flat 25% for Federal (assuming it is less than $1,000,000).  You can ask your employer which method they use.

If they take the flat 25%, changing your W-4 won't do anything.  If they base it on your W-4, then changing it WILL reduce what they withhold.

It sometimes takes a while for the payroll department to change the W-4, so if you do change it, you should do it as soon as possible.

OK, thanks.  I heard 25% the first time I asked HR, and then the manager told me to "check with my tax advisor".  So, truly I won't know the effect of the tax on the lump sum and overall until I file again at the end of 2017 and what employment I get in 2017...