Can I extend my 60-day tourist exempt stamp in Thailand using my new passport?

I am currently in Thailand on a 60 day tourist exempt stamp which I would like to extend for 30 days, with the aim of doing an in country conversion to a Non B visa.

My question is about transferring to a new passport as the current tourist exempt stamp is in my old passport but I would like to go forward with my new passport.

Can I just go to IT square Lak Si with both passports, apply for the 30 day extension as normal and then request for the extension stamp to be done in my new passport?

I have a letter from my embassy about transferring to a new passport.

(There are only 3 months left in my old passport)

Thank you