We've enabled our beta of Box support for all Frame Personal, Frame for Education and Frame for Business accounts. If you are on a Frame Platform account you can have the Box beta enabled by request (just send a note to email@example.com).
From the Files page in your Launchpad you'll see the Box (and Google Drive) options are now enabled in addition to Dropbox, letting you connect your account there. In addition, you can connect from within a session by clicking the Box icon in the Frame status bar (lower right corner). Let us know what you think.