To increase Brix levels, make sure the tree is fully mature before allowing it to hold fruit. Also make sure your tree gets maximum sun exposure and don't overwater your tree. In the agriculture industry, they will do plant and soil analysis so that they know what nutrients or elements are required by the tree.
As a backyard orchard grower, you can follow my above recommendations and also thin about half of the set fruit off your tree so that your tree can concentrate its resources on fewer high quality fruit. If you are not currently fertilizing your tree, you can add some Potassium, Calcium, minute amounts of Boron but it gets very detailed so it may be easier to feed about once a month with an organic fruit tree fertilizer. I've found organic fertilizers are more forgiving and easier to use for newbies. I also use Azomite to replenish my soils.
Simon