Is there a grace period for L1 to H1B

I am in USA currently on L1 with company ABC. My L1 visa is expiring in Feb 2024. I earlier had come to USA on H1B and have an approved I140 with the same employer ABC. I am requesting my employer ABC to switch over to H1b . My question is , can I stay in USA and continue to work with ABC while my change of status from L1 to H1b is in progress and the approval comes after Feb 2024?

Thanks in advance for your reply.