Exchange 2013 can be installed in an Exchange 2010 organization and you can have a number of Exchange 2010 CAS arrays and DAGs coexisting with a number of Exchange 2013 CAS arrays and DAGs.
You'll need to configure the CAS co-existence with the same concepts as you did for the single server migrations.
As for mailbox moves, you can move mailboxes from mailbox databases in the Exchange 2010 DAG to the Exchange 2013 DAG.
Once done, public folders need to be migrated then the Exchange 2010 environment decommissioned.
Note that this is a very abbreviated set of steps. More detailed steps can be generated using the Exchange Server Deployment Assistant which is here: https://technet.microsoft.com/en-us/office/dn756393.aspx?f=255&MSPPError=-2147217396
Thanks.