  The $t$-adic symmetric multiple zeta value is a generalization of the
symmetric multiple zeta value from the perspective of the Kaneko-Zagier
conjecture. In this paper, we introduce a further generalization with a new
parameter $s$, which we call the $(s,t)$-adic symmetric multiple zeta value.
Then, the $(s,t)$-adic version of the $t$-adic double shuffle relations,
duality and cyclic sum formula are established. A finite counterpart of the
$(s,t)$-adic symmetric multiple zeta value is also discussed.
