Yes, you can. This is called Transposition cum Dematerialization. The joint holders are entitled to change the sequence of names by making a written request to the company. This does not constitute a transfer of holding of rights. Changing the sequence of joint holders is called 'Transposition'. However, transposition facility can be availed for entire holdings in a folio and not allowed for part of the holdings.

If the same set of joint holders hold securities in different sequence of names, then there is no need to open multiple demat accounts for dematerialization of such securities. Using 'Transposition cum Demat facility' such securities held vide certificates in different combinations, can be dematerialized in one demat account. For this purpose, Dematerialization Request Form (DRF) and an additional form called 'Transposition cum Demat Form' should be submitted to the DP. This is explained in the diagram below

Also Read

Can I de-materialize shares held by a single owner into a joint demat account?

How to demat jointly held physical shares if one of the holders is deceased?