Under a non-exclusive agreement, you are not assigning any permanent rights to the other party - you still own everything. Therefore, you will still be able to do other non-exclusive agreements. You should also be able to sign an exclusive agreement for the same song as well, but you must tell the party to whom you are signing the exclusive agreement about previous non-exclusive agreements.

For example, you sign a non-exclusive agreement with 123 PICTURES INC.

Then, XYZ
FILMS INC. offer you a non-exclusive agreement for the same song which you also sign.

Finally, HAPPY COSMETICS CO. want to use the song in a worldwide advertising campaign but insist on exclusive ownership (this would be unusual but this is just hypothetical !). You inform them of your two previous agreements and as long as they are OK with it, you sign an exclusive agreement with them for that song.

After that date, you can no longer license this song to anybody else because of your exclusive agreement with HAPPY COSMETICS CO.