i had 3 fig trees competed for space in my tricho garden. brown turkey, kadota & one called green stripe (or thats what i called it)
green stripe grew like a rocketship with few fruits, but boy were they ever tasty, somewhat like strawberry jam. I kept whacking it back & it kept throwing numerous branches with few figs.....Boom! it went bye bye real quick
kadota was a heavy producer with a very sweet taste & the fruits would ferment if not picked relatively quickly. I whacked it back to the main stem every year and it came roaring back each spring. I finally dug it up & gave it to a friend, the trunk was around 3-4" in diameter at the time.
brown turkey: this one is by far the best of all, however the green japanese beetles love it to death. The plant gets whacked back (severely) 1 or 2 x yearly and it comes roaring back each time. I limit its height to 7-8' max, forcing it to bush out. I will either have to net it this yr to keep the beetles at bay or dig it up & toss it. Its taking up valuable real estate where i could be growing more trichs
from my fig trees I've made fig jam & fig 'leather', not to mention bags of figs stored in the freezer.... you might say I'm all figged out....
If you want more side branches, forget bap, forget chemicals; just whip out your pruning shear & start whacking away. Top the main stem & cut every branch back. I'd advise pruning in the late fall although you could prune most anytime.