Look at the 612 DVR and 211K receiver. Each counts as only one output, but the 612 actually has 3 tuners (2 sat and 1 ota) and the 211k has 2 tuners (1 sat and 1 ota).
For instance if you had 3 612's (A,B and C) you could run component HD to TV#1 and HDMI to TV#2 from 612 A; same to TV##3 and TV#4 from 612 B; and same to TV#5 and TV#6 off 612 C.
Of course the TV's sharing a receiver will both be watching the same programming, but if you get 4 612's for 6 TVs, two of the 612s will be servicing only 1 TV.
If you need more tuners, they will have to be purchased.