  We consider the Thompson-Stein group F(n_1,...,n_k) for integers n_1,...,n_k
and k greater than 1. We highlight several differences between the cases k=1$
and k>1, including the fact that minimal tree-pair diagram representatives of
elements may not be unique when k>1. We establish how to find minimal tree-pair
diagram representatives of elements of F(n_1,...,n_k), and we prove several
theorems describing the equivalence of trees and tree-pair diagrams. We
introduce a unique normal form for elements of F(n_1,...,n_k) (with respect to
the standard infinite generating set developed by Melanie Stein) which provides
a solution to the word problem, and we give sharp upper and lower bounds on the
metric with respect to the standard finite generating set, showing that in the
case k>1, the metric is not quasi-isometric to the number of leaves or caret in
the minimal tree-pair diagram, as is the case when k=1.
