  A tableau inversion is a pair of entries from the same column of a
row-standard tableau that lack the relative ordering necessary to make the
tableau column-standard. An $i$-inverted Young tableau is a row-standard
tableau with precisely $i$ inversion pairs, and may be interpreted as a
generalization of (column-standard) Young tableau. Inverted Young tableau that
lack repeated entries were introduced by Fresse to calculate the Betti numbers
of Springer fibers in Type A, and were later developed as combinatorial objects
in their own right by Beagley and Drube. This paper generalizes earlier notions
of tableau inversions to row-standard tableaux with repeated entries, yielding
an interesting new generalization of semistandard (as opposed to merely
standard) Young tableaux. We develop a closed formula for the maximum numbers
of inversion pairs for a row-standard tableau with a specific shape and
content, and show that the number of $i$-inverted tableaux of a given shape is
invariant under permutation of content. We then enumerate $i$-inverted Young
tableaux for a variety of shapes and contents, and generalize an earlier result
that places $1$-inverted Young tableaux of a general shape in bijection with
$0$-inverted Young tableaux of a variety of related shapes.
