Hopefully, there's a very "simple" answer to this question:
- Can a SQL Server 2012 subscription database in a transactional replication setup also be used for publication?
Yes you can but not easy to maintain. If your ever get out of sync and you have to reinitialize, resnap of the first set of publication and subscription; you will need to remove the publication property of the subscription. Otherwise you cannot do a full snapshot.
It sounds like you might need to consider Peer to Peer Replication. You didn't provide too much info on the current setup.
See if this address your needs: https://docs.microsoft.com/en-us/sql/relational-databases/replication/transactional/peer-to-peer-transactional-replication
It almost sounds like you want to implement multi-master replication. But not quite, as from the comments, I gather you want to filter the re-publication? Otherwise, you could have just added another subscription to the original publication... See this for more information: https://docs.microsoft.com/en-us/sql/relational-databases/replication/publish/replication-publishing-model-overview
There is nothing stopping you from doing this, as you could just use the existing Distributor, and a filtered publication will work on the re-published database, as it would be a separate transaction-log. But "chaining" this type of topology is like asking for trouble...as alluded to earlier, a management-nightmare!