Ordering mountpoints

Generally the order of resolving a filename is the order in which you mounted the filesystems at the same mountpoint (i.e., new mounts go on top of or in front of any existing ones). You can specify the order of resolution when you mount the filesystem. For example, you can use:

the before and after keywords for block I/O (devb-*) drivers, in the blk options
the -Z b and -Z a options to fs-cifs, fs-nfs2, and fs-nfs3

You can also use the -o option to mount with these keywords:

before: Mount the filesystem so that it's resolved before any other filesystems mounted at the same pathname (in other words, it's placed in front of any existing mount). When you access a file, the system looks on this filesystem first.
after: Mount the filesystem so that it's resolved after any other filesystems mounted at the same pathname (in other words, it's placed behind any existing mounts). When you access a file, the system looks on this filesystem last, and only if the file wasn't found on any other filesystems.

If you specify the appropriate before option, the filesystem floats in front of any other filesystems mounted at the same mountpoint, except those that you later mount with before. If you specify after, the filesystem goes behind any any other filesystems mounted at the same mountpoint, except those that are already mounted with after. So, the search order for these filesystems is:

those mounted with before
those mounted with no flags
those mounted with after

with each list searched in order of mount requests. The first server to claim the name gets it. You would typically use after to have a filesystem wait at the back and pick up things the no one else is handling, and before to make sure a filesystems looks first at filenames.