In five months from seed my P. Incarnata have become monsters. I planted them about 3 feet apart and have trellis on opposite sides. They grab each other in the middle and climb together to form a mass of flowering plant with so many fruit I lost count. The hundreds of caterpillars do little if nothing at all to slow their growth. You can be surrounded with butterflies all day. With the way these are growing I don't understand what you mean by making them more branchy. I think one vine could probably cover a house with uncountable branches on its own. When a caterpillar eats a tip the rest of that vine does start to grow a lot more vines from it though.

Your passionflower will grow upwards first and then have branches. Many Passion flowers bloom from newer growth, probably best to let it grow. If you do not have it in a sunny spot it will appear lanky until it grows enough to reach sunlight, then branch out.

Perhaps it makes difference that my incarnata are of variety "Incense".

Many dozens of them now, many hundreds over several years.

Most of them continue forever as one stem.

In nearly every instance in which a branch does grow,
the plant sooner or later neglects one of the two branches,
which becomes bare then dies. Plant continues to grow productively.