Dear aspirant hope you are doing well...

yes of course you can give Improvement exam of hsc board . You can check out the dates from the official website of Maharashtra State board.

https://www.mahahsscboard.in/statisticshsc.htm

Maharashtra State Board of Secondary and Higher Secondary Education, Pune has uploaded the HSC Marh Exam Time Table on the official website mahahsscboard.maharashtra.gov.in. The HSC Examination for session year 2021-22 will be held in March- April 2022.

Hope it's helpful thank you