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http://www.operationbarbarossa.net/the-staraya-russa-offensive-operation/
Historically the Soviets mounted an offensive in the first half of August 1941 against the flank of AG-North, targeting 16th army to relieve pressure on Leningrad, as the Germans were massing 4th Panzer Group to jump the Luga River Line and take Leningrad. Instead as the Soviets attacked they panicked AG-North's commander, von Leeb, diverting 56th Motorized Corps to assist 16th army. In the process they destroyed most of new Soviet 34th Army, which had bogged down badly in swamps and due to logistics being very inadequate. It would seem had the Germans just left the Soviet offensive to peter out on it's own due to logistics, they could have kept a fully massed 4th Panzer Group together to drive on Leningrad and potentially take it in August. But the diversion killed any chance to seriously take the city and all that was gained was a tactical victory and pilling up more Soviet PoWs and dead. It also pushed the 16th army further East to Demyansk and left them vulnerable to the Winter Counteroffensive.
What if von Leeb did not consider the threat of the Soviet offensive against 16th army an existential danger and just pushed ahead against Leningrad in early/mid-August instead, leaving 16th army to check the Soviets and when available help sent from 3rd Panzer Group, already engaged in operations further south? Could Leningrad have been taken? Would the Soviets have managed to push any further west or encircle parts of 16th army?