H1B COE petition - can I continue working at present employer?

[petitioning_individual]

I have an approved H1B COE petition from a new employer, but they are unable to let me start before the 60 days expire (due to restrictions on when they onboard new employees).

Can I continue to work at my present employer (which has a valid I-797 for me) even past 60 days since the approval of the COE petition? They are filing an amended petition to change the start date, but I don't know whether I can continue working here in the meantime.

Thanks!