Payroll overlap with two employers

Hi, I am on H1B
Currently working for Desi Employer,
got a offer from the new Client, H1B transfer approved. They asking me to join ASAP, mostly Dec 21, 2022, but I haven’t given the 2 weeks notice to my current desi employer.

If I join the new cilent, start working and then give 2 weeks notice to my current employer, then payroll from the both client may overlap for 2-4 weeks which means 2 paystubs.

Any future issues occur with this paystyb overlaps ? Or it totally fine with 2 paystubs overlap or please give me some insight and provide any other thougths if you have.

Thanks in Advance!