You already have Die Linke.
Lafontaine & Co never managed to turn Die Linke into a Left SocDem party. It has too much bagage and its very existence blocks the advance of a credible leftist alternative.
I was speaking of Jeremy Corbyn more specifically.
It remains to be seen if left-wing social democrats can appeal to a broader audience generally, anyway. Throw in the Greens and they're already at 20%. Outside of Greece, where has a party to the left of mainstream social democratic party done better than that? Even Podemos is polling in that range.
Most usually, such parties struggle to get over 10%. Their room for improval is questionable.