Yes! Once you're on the video you would like to share in the My Videos page, select Video Settings from the upper-left corner. These settings allow you to add subtitles and share ownership of the video.
To share ownership of this video, simply enter their Zaption email address. You can also remove ownership of the video in this tab.
Once you've granted access, the video will be available on the My Videos pages and My Videos tab of the Add Videos modal for the user.