To put weight on my hard keeper (and hyper half Arab) I used alfalfa pellets, flax, and a vitamin supplement. I feed two 3 qt scoops of alfalfa pellets a day (about 6 lbs by weight), 1 cup of flax (whole or ground/milled), and NutriPlus++
(1oz serving). Plus free choice hay/pasture. It worked like a charm!! I use apple cider vinegar to make it all stick (also aids in digestion).
If you want to keep feeding beet pulp, I would recommend feeding 3 lbs a day (dry weight) with one 3qt scoop of alfalfa pellets (3lbs) mixed in.