DLA appeal/ new claim

Hi, apologies if this has been asked before, I applied for DLA in May, was turned down, asked them to look again at decision, turned down, now going to appeal decision but wondering if I can put in a new claim now? I dont want to be another 3/6 months down the line with no progress.

Yes you can. You can have claims and appeals running concurrently if you wish?

does the above only apply if you where awarded nothing at all or can you still start a new claim if you where awarded low rate care only but want to appeal for a higher rate?