No, Mesa 7i80 does not go with 7i77 and 7i85, the Mesa 7i92TM goes with those. 7i80 is 50 pin, 7i92 is 25/26pin.
There are other options also, the 7i77 is hard to find so a bit more searching is needed, on the 50 pin stuff i can not help, but for 25 pin stuff i used a lot, here are some options:
-7i97T it is roughly the same as 7i92TM with 7i77, with 7i85 or even better with 7i74 as this needs plain LAN cables to wire the 7i70 (48 inputs) and/or 7i71/7i72 (48 outputs sinking or sourcing), or 7i84 (32 in and 16 out)
-7i92TM (notice the M, makes it directly plugable into 7i77 so no need for IDC26 to DB25 cable and adapter), with 7i85 OR 7i74
-7i96S (step/dir and spindle) with 7i83 (analog outputs) and 7i85 (encoder and SSerial) for 7i70/7i71/7i72/7i84
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I think there is also 7i93 IRC should have 3 of IDC26 headers, but not sure, should be same as 7i92 with more IO. Again, do double check this.