No. Apple has specifically restricted the ability for app developers to move this type of storage onto external drives in newer versions of iOS. I've avoided updating from Monterey for over a year now because the update specifically breaks Dropbox's ability to do this https://bsky.app/profile/jerryactually.bsky.social/post/3l7lhalgfhm24
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But, looks like they got on board and made it happen: https://help.dropbox.com/installs/mac-external-drive-support