double coated breeds can also itch if they are moulting and if they are too warm.
As rona mentioned it is the season for harvest mites but these mainly affect the feet.
Chappie is a good food for those suffering sensitive skin but it does seem to coincide with the itchyness so may be a cause?
Dont no what the protien content is in chappie dry but ideally the lower the better, something like 20% or less as too hi protien in the diet can also make them itch.
Is it a general itch or 1 area? if one area and chewing them selves it could be a sign of pain/discomfort...round the tail could b anal glands over joints may be arthritis.
GSD's can be prone to things like wet eczeama so would check for any sore sticky lesions, clip the fur to let the air at it and take back to vets for steroid and antibiotic treatment.
The trouble with skin probs what starts with a minor irritation can soon progress into a chronic nightmare, the itchy skin gets damaged becomes open to infection that gets in and continuall trauma through sctratching prevents the skin from healing.
Try if u can to stop the scratching, if using feet bandage the paws or put sox on to minimise the damage if chewing bascket muzzle or elizabethan collar to prevent access to sore area's. Old t-shirts are also good instead/aswell as the paw covering.
U can also use antihistamines but check with ur vet they are happy for u to try.
Lastly Aloe-vera...great to apply topically to any sore area's as very soothing and can also be given orally for upset tums.
Omega oils (mackeral, sardines or pilchards in oil once a week) great for skin or use evening primrose capsules daily to keep the skin healthy.