  The domination multisubdivision number of a nonempty graph $G$ was defined as
the minimum positive integer $k$ such that there exists an edge which must be
subdivided $k$ times to increase the domination number of $G$. Similarly we
define the total domination multisubdivision number msd$_{\gamma_t}(G)$ of a
graph $G$ and we show that for any connected graph $G$ of order at least two,
msd$_{\gamma_t}(G)\leq 3.$ We show that for trees the total domination
multisubdivision number is equal to the known total domination subdivision
number. We also determine the total domination multisubdivision number for some
classes of graphs and characterize trees $T$ with msd$_{\gamma_t}(T)=1$.
