Qatar -- of course it is feasible. I have kept a copy of the Seattle Post-Intelligencer 777 special suppement, dated April 9, 1994, which has 16 pages on the new Boeing airplane. On page 3, they show some typical interior layouts, and one has a so-called business section with 2-4-2, as you suggest. That configuration includes 24 first class (2-2-2), 61 business class (2-4-2) and 243 economy class (3-4-3 -- that's tight!) for a total of 328.
Not having the cabin dimensions handy, I can make some assumptions. Taking the economy section above, multiply by 0.8 to get 8 across instead of 10, then by 0,9 to get 33" instead of 30" pitch, that leaves about 174 in the back. The center can stay at 61. The front section can accommodate about 6 rows, for 48. The total then would be about 283.
This is very rough estimate, of course, but is a bit shy of 300, Arsenal suggests.
"In God we trust, everyone else bring data"