Hello sir , sorry for late response. Happy Diwali :)
as i'm able to see , if there is condition like 'No additional space avail' then i don't think that this work can be done in constant time...if there is again condition like only PUSH is allowed , no POP then , using some temp variable we can certainly tell MAX in const time but when 'in b/w' POP is going on , we can't tell MAX in O(1) unless we use some additional stack like Rishabh answered...
I'm not that good with programming , please tell me if i went wrong somewhere.