  We construct multiple $qt$-binomial coefficients and related multiple
analogues of several celebrated families of special numbers in this paper.
These multidimensional generalizations include the first and the second kind of
$qt$-Stirling numbers, $qt$-Bell numbers, $qt$-Bernoulli numbers, $qt$-Catalan
numbers and the $qt$--Fibonacci numbers. In the course of developing main
properties of these extensions, we prove results that are significant in their
own rights such as certain probability measures on the set of integer
partitions.
