When initiated, accounts that the new iteration supports at the time are migrated.
For instance, if you have stories from Facebook in the legacy app, but the new iteration doesn't yet support Facebook stories, then the migration tool will not migrate the Facebook data in the legacy app until the new iteration supports it.
When the new iteration does support the account, you will need to migrate your data again. Doing so you should not lose any existing data in the new iteration. It will all merge together.