If you were not allowed to change it under any circumstances, it ought to be impossible. But you can. However, you should be aware of the security implications. If you set it too loose, people will be creating private files in their home directories which are readable by anyone -- if that's acceptable then go ahead. (Setting it tighter than the default is usually not a problem.)

Sounds like you might be barking up the wrong tree, though. Could you describe what problem you are trying to solve? If you want files in a shared directory to be created with specific permissions, maybe your platform would offer a facility for this by other means (for example, by using the setgid bit on the directory, on some platforms).