Really there should be a way of running booked portion workings so that a through service between Manchester and Chester via Altrincham with a split at Stockport. It probably wouldn't work in the morning going towards Manchester but should work in the evening if they have the Stockport departure time a few minutes after the arrival time, which wouldn't be ideal but would be better than a risked missed connection.
Currently the 08:56 arrival from Chester occupies Stockport Platform 4 for 11 minutes, waiting for its ECS path across Heaton Norris Junction to Newton Heath. So there would be plenty of time to couple it to a Piccadilly-bound unit instead. Northern has a path to Piccadilly at 09:07, but unfortunately that is used by the 09:04 arrival from Alderley Edge, which is a 323 diagram.
Around 17:00 and 18:00 the three southbound platforms at Stockport are heavily utilised, and I doubt that extra dwell time for splitting could be accomodated on a regular basis. There are six southbound departures in 15 minutes, the xx:51 to Alderley Edge/Crewe (Platform 1), xx:54 to Norwich/Nottingham (Platform 0), the xx:55 to Stoke (Platform 1/2), the xx:58 to Chester (Platform 2/1), the 16:58/18:00 to Buxton (Platform 0) and the xx:04 to Euston (Platform 2).
The signallers' priority is, of course, to get the Chester train out the way, across Edgeley Junction, in time to avoid delay to the following Virgin express. The May timetable recast advanced the Stoke service by 3 minutes and gave it a Fast line path from Piccadilly, while the Buxton service has a Slow line path and the Chester unit arrives ECS from Heaton Norris Junction. The pathing conflicts have resulted in frequent last minute platform interchanges between the Stoke and Chester services. These confuse passengers, many of whom seem deaf to the PA announcements and unable to distinguish a 142 from an 323. Sometimes passengers have already boarded before the PIDs catch up with the change, so there is an increased risk of people having to wait an hour at Navigation Road for the next service back to Stockport.