dual w-2 and 1040ES for household employees

I have a situation where I pay household employees (to care for elderly MIL), and may need to use 2 payroll vendors in the same year.
Both would pay some estimated employment taxes to the IRS, would both would pay our employees regular, payroll, Medicare, SS taxes as well.
The existing vendor issued our employees w-2 and estimated taxes to use last year to help us do our 1040 Schedule H.
End of this year we'd have both vendors issue w-2 to employees and send their own estimated tax payments on our behalf to state/federal govts. So employees would get dual w-2 from same employer just because of a systems issue on our end, and we'd have 2 sets of estimated payments to consolidate to our schedule H. I would be very beneficial to NOT wait for end of the year to start using the new payroll vendor, and maybe even continue using both next year (each would pay a portion of the payroll possibly to same employees to continue dual w-2 the following year).

Anyone see were this dual issuance of W-2 to employees (or schedule H ES payments) would cause employees or employer any tax problems ?

Thanks for sharing if you have had experience with this.