Cathie

You can only grow new branches on trees if the tree decides it wants to grow one there, though you can encourage new ones wherever by chopping back the trunk (or foliage in general), though whether the new ones grow where you want them is mostly up to the tree, and whether they'll grow below the existing ones depends on the species and the individual tree. Of course they'll thicken, but no more or less than others on the tree of a similar age. The only way to control the thickness would be either to continue training the tree as a whole (and the new ones will eventually grow into their 'place' appropriately) or kill the tree to stop further growth. Of course you can always graft branches onto the tree, but you still won't be able to control thickness once it takes.