Let
$C_c^{*}(\mathbb{N}^{2})$
be the universal
$C^{*}$
-algebra generated by a semigroup of isometries
$\{v_{(m,n)}\,:\, m,n \in \mathbb{N}\}$
whose range projections commute. We analyse the structure of KMS states on
$C_{c}^{*}(\mathbb{N}^2)$
for the time evolution determined by a homomorphism
$c\,:\,\mathbb{Z}^{2} \to \mathbb{R}$
. In contrast to the reduced version
$C_{red}^{*}(\mathbb{N}^{2})$
, we show that the set of KMS states on
$C_{c}^{*}(\mathbb{N}^{2})$
has a rich structure. In particular, we exhibit uncountably many extremal KMS states of type I, II and III.