Probably many a reason why this would not work, but, if a high capacity Birmingham -> Manchester service was to be desired, perhaps TfW services which currently run to Birmingham International could be curtailed to run to Wolverhampton only.
These trains are low capacity in comparison to most that run to Birmingham, and could terminate in platform 6 at Wolverhampton. Local services Shrewsbury <-> Birmingham would still provide a direct, albeit slower service, and passengers could change for the many trains available at Wolverhampton to Birmingham.
Then, the service to Manchester could hopefully operate as an 8-car set of 350/2's run in the TfWs path both northbound and southbound and terminate at Birmingham International (arriving XX:52, departing XX:08).
The northbound Bournemouth<->Manchester currently arrives at Birmingham International at around XX:40, and the next Southbound departs at XX:13. There appears to be nothing through platform 5 during this time, so perhaps it could terminate in platform 5 with the northbound forming the next Southbound service running Birmingham International<->Bournemouth.
Hopefully, if this change was made it would (if adequate train crew was recruited) allow for the Bournemouth<->Birmingham International service to run consistently as double voyagers, with the 350/2s providing increased Birmingham<->Manchester capacity.