You know 10 channels are on 10 different frequencies? You will need 10 tuners to bring in those different frequencies.
Then, since it's digital TV, each channel has separate sub-channels or streams. (They have different names in each country's TV system and the broadcasters themselves may use different names too.) A regular PVR is able to split out those streams and save them as an MP4 file. Usually it can only save one or two because there's so much data.
There's other information alongside the streams, such as the onscreen program guide. I never heard of anyone recording that.
So 20-40 PVR boxes should do the trick for you, for the video at least.