I think you could do this with replication filters and multiple datasets.  This does have a limitation on retention polices.  Hopefully its minor for you..

For Example:

1. Create two datasets.  One with data you want replicated and one without.

2. Create two retention polices.  One with basic retention and one with advanced retention.

3. Create two groups using the new dataset and retention.  Put client in both groups.

     - For example the one you replicate off site uses basic retention and the one that doesn't uses advanced retention.

4. Create a replication group that doesn't replicate untagged backups.

The client will be backed up twice with the different datasets sequentially.  I do not know if there is a downside to the synthetic aware backup process being the clients data is completely different each time it backs up.  ,My guess is no because other datasets like BMR produce 2 separate jobs.

This would be a tricky one to pull off.

It's not possible to exclude bits and pieces of a backup during replication because of the way Avamar stores backup data. The backup is stored in a tree structure and removing any piece of that tree would damage the integrity of the backup.

You'd have to ensure that the folder you wanted to exclude from replication would be backed up by itself. Because the replicator would have no way to differentiate these backups from the regular client backups, you'd have to run the backups for the second dataset to a different client account. The only practical way I can think of to make something like this work would be to install a second avagent but this is only possible on some operating systems and -- unfortunately -- it's not officially supported.