John,
Without seeing your canoe closer, this is only a guess, but I suspect that you will be OK with just the 2 center thwart.
This opinion makes 2 assumptions, 1) that your model is 16 ft or shorter, and 2) that is has the usual "robust" Chestnut gunwales.
The thwarts and gunwales are what gives the canoe shape and rigidity, longer canoes with "thinner" gunwales need more thwarts, and shorter canoes with "thicker" gunwales need fewer.
17 and 18 ft'ers usually have 3 thwarts/yokes, the 2 quarter thwarts and the center thwart or yoke. 16 ft'ers often only have the 2 quarter thwarts , or 1 and a yoke. 15 ft'ers may only have a center thwart/yoke.
On a 16 ft Thompson I did, I put in only a center yoke and left the 2 quarter thwarts off, BUT I used slightly larger gunwales to offset the reduced support from less thwarts, it's doing just fiine.
Dan