  With nucleons occupying several shell model $j$ orbits, the isovector pair
creation operator $A^1_\mu$ (creates a two particle state with angular momentum
$J=0$ and isospin $T=1$) is no longer unique. Choosing it to be a sum of
single-$j$ isovector pair creation operators each with a phase, there will be
multiple pair $SO(5)$ algebras with isospin; with $r$ number of $j$ orbits,
there will be $2^{r-1}$ $SO(5)$ algebras each with a corresponding
complementary $Sp(2\Omega)$ algebra [$2\Omega = \sum_j (2j+1)$] that gives
seniority and reduced isospin quantum numbers. Three applications of multiple
$SO(5)$ algebras are presented demonstrating the usefulness of considering
$SO(5)$ pairing algebras with general sign factors.
