Systems and methods are described for efficiently performing various operations at the granularity of a consistency group (CG) within a cross-site storage solution. An example of one of the various operations includes an independent and parallel resynchronization approach that independently brings individual volumes of a CG to a steady state of in-synchronization (InSync), thereby contributing to scalability of CGs by supporting CGs having a large number of member volumes without requiring a change to the resynchronization process. Another example includes preserving dependent write-order consistency when a remote mirror copy goes out-of-synchronization (OOS) for any reason by driving all member volumes OOS responsive to any member volume becoming OOS. Yet another example includes independent creation of snapshots by member volumes to support efficient and on-demand creation by an application of a common snapshots of all or a subset of peered member volumes of a CG with which the application is associated.