Trying to map some of this out with real numbers...
Next year's cap should be $149,623,100. The second apron should be around $201,073,400, assuming it goes up 10%.
We have $136,761,750 in committed salaries next year for ten players. This doesn't include Pritchard's qualifying offer.
If JB's salary next year is a straight 35% of the cap, it would be $52,368,085.
Adding that to committed salary, we'd be at $189,129,835 with 11 players under contract.
That would give us $11,943,565 in room to fill out the roster by adding three or four players.