Is it possible to increase the prune size and get bitcoind to pull previous blocks?
Bitcoin Core doesn't have such a feature. The prune depth controls how many blocks are kept, and you can change that (-prune=N option on the command line or prune=N in bitcoin.conf), but once a block is pruned, it is gone. If you want to add blocks back, for now you'll need to resync from scratch.
There is no technical reason for this; it's perfectly feasible to implement a mode where desired old blocks are refetched and inserted into the blocks datadir again, but this simply isn't implemented at this point.