Moonlighting for a month

I work in TCS and I have received an offer from a PBC but they want me to join early ( by end of this month ) but my last working day is on 4th Aug.

My manager is ready to release me early i.e by end of Jun and is also discussing with upper leadership for early release. But in case they reject early release I am planning to onboard to the PBC and work in both companies for a month till my lwd.

My TCS timings are 1-10pm ( plus office is nearby )and for the other it is 9-5 plus I won’t have much work in TCS. For this I have to inform the other HR. So will they agree to this and what will be some issues that we face?!