I do not see any OOTB activities having such functional behavior. Bulk actions has functionality to transfer set of assignments to single operator/another workbasket but not to multiple operators. But you can recreate something similar to "GetNextWork" functionality. Although this a pull based mechanism for the operators. You can follow the below approach for push based-
1. Loop over the assignments from the workbaskets of the workpool (can use FindAssignmentInWorkBasket as reference)
2. Examine which assignment is suitable for which operator in the current work pool.
3. Then you can perform transferAssignment which would internally call reassign activity.
You will have to ensure that the reassign to any operator should happen based on some criteria like skillset of the operator, availability.
But we are using single assignment through which we are populating the data from Work basket. As you mentioned using push based, Will the same Workobject will transfer to user 1 and user 2 ? Without using the parallel flows?