  Set multipartite Ramsey numbers were introduced in 2004, ge-neralizing the
celebrated Ramsey numbers. Let $C_4$ denote the four cycle and let $K_{1,n}$
denote the star on $n+1$ vertices. In this paper we investigate bounds on
$C_4-K_{1,n}$ set multipartite Ramsey numbers. Relationships between these
numbers and the classical $C_4-K_{1,n}$ Ramsey numbers are explored. Then
several near-optimal or exact classes are derived as applications. As the main
goal, polarity graphs from projective planes allow us to find suitable
subgraphs which yield some optimal classes too.
