H1B Stamping in India with 2 Petitions

I have a valid petition (I-797) expiring on 25th Aug’2023 and blocked the Visa appointment for the same at Chennai consulate at 25th May’2023. Can I initiate the H1B extension (Premium) now and use the latest approval (to be received) for the existing visa appointment blocked for 25th May’2023? Please note the new approval notice may start valid from (26th Aug’2023).

Absolutely yes. Just submit updated DS-160 with the new I-797 and carry both current and new I-797 to your interview or submit with other dropbox documents.