Probably the best approach. It comes down to what your goals and budget are.
Carrying capacity largely comes down to the following....
3/16" tubing (ID) cross-sectional area = 0.028 sq inches
5/16" tubing (ID) cross-sectional area = 0.077 sq inches
1/2" pipe (OD), 0.622" (ID) cross-sectional area = 0.3 sq inches
3/4" pipe (OD), 0.824" (ID) cross-sectional area = 0.53 sq inches
So having three 3/16" tubing lines run into one 5/16" might work, but it might also be maxed out during peak flows. 1/2" or 3/4" pipe would also work. Using three 3/16" runs is also doable and probably about the same cost as 1/2", but easier to install and ensures that you don't have all your eggs in one basket. If there is a leak on one line it won't affect the other two lines.