You can prune the tree while it is dormant in winter or in summer. Dormant pruning is pruning the tree during the late winter, when no new growth is happening and the tree doesn't have any leaves. Pruning while the tree is dormant encourages vibrant growth come spring, and it's less likely to cause damage to the tree than summer pruning. Summer pruning can be used to slow the growth of a tree that is getting too big and to thin new growth that is overcrowding. If your plum tree is getting too big for your yard, you can prune in the summer to slow down its growth. Whereas dormant pruning encourages vibrant spring growth, summer pruning cuts away the tree's energy and limits growth for the season. Beware that summer pruning can cause the tree to put its energy into leaf growth rather than fruit production

It's important to prune a young tree during its first dormant season to encourage good growth and a suitable shape. Create a scaffold whorl. Choose four branches evenly spaced around the tree to serve as the tree's "scaffold whorl." These branches provide structure and keep the tree's shape balanced. Cut each of the four branches back so that each one has just 1 or 2 buds. Make the cuts just above the buds. Cut the remaining side shoots and branches flush against the trunk.

Cut back the suckers. Suckers are new shoots that come up from the root system around the base of the tree. Cut them away so that the tree's energy is directed into the main tree trunk and won't get sapped by the suckers. Cut the suckers all the way to the ground using loppers.

Suggest you cut the middle trunk this year, see how the tree responds. Next year consider eliminating a second trunk.