exFAT, as an extension of FAT, is not capable of storing discretionary access control metadata. This is why all the files on an exFAT volume appear to be 777 permissions. It's basically saying "this volume is wide-open because we can't not make it wide-open due to the file system format".
The short answer is no. The long answer is that you can create another filesystem within the exfat file system using, e.g.
dd (to create a sparse file) and then use filesystem-specific tools to create a filesystem on the file. Then you can mount it. The Mac OS X HFS+ native filesystem would work fine, since your
/ volume is definitely capable of discretionary access controls and any other filesystem features that OS X relies on. But that won't be portable across platforms (maybe to Linux, but not to Windows).