No, the new employer is required to withhold Social Security tax, without considering what the previous employer withheld. There is no way to prevent it. The excess Social Security tax will be applied as a credit on your tax return at the end of the year. That's how you get it back.
As Opus 17 suggested, you could reduce your income tax withholding to compensate for the extra Social Security tax, so that you don't have to wait until you file your 2019 tax return to get it back. Two cautions if you do that. (1) Make sure your new employer reduces only your federal tax withholding, and not the state tax withholding (if you are in state that has state income tax), because the excess Social Security tax does not apply to your state tax. They will probably want you to fill out a separate form for state withholding. (2) Make sure you adjust your withholding again at the beginning of 2020, since you will not have the credit for excess Social Security tax for 2020.
