You can say 

> 1) Do you have more classes today?
> 
> 2) Do you have any classes today?
> 
> 3) Do you have other classes today?
> 
> 4) Do you have any more classes today?
> 
> 5) Do you have any other classes today?

> 6) Do you have another class today? (Thank you @Simon F)
> 
> 
> 7) Do you have (any) further classes/class today?
> 
> 8) Do you have (any) additional classes/class today? ( Thank you @Mr Lister)