For a simple undirected graph \(G\) with vertex set \(V\) and edge set \(E\), a total \(k\)-labeling \(\lambda: V \cup E \rightarrow \{1, 2, \ldots, k\}\) is called a vertex irregular total \(k\)-labeling of \(G\) if for every two distinct vertices \(x\) and \(y\) of \(G\), their weights \(wt(x)\) and \(wt(y)\) are distinct, where the weight of a vertex \(x\) in \(G\) is the sum of the label of \(x\) and the labels of all edges incident with the vertex \(x\). The total vertex irregularity strength of \(G\), denoted by \(\text{tus}(G)\), is the minimum \(k\) for which the graph \(G\) has a vertex irregular total \(k\)-labeling. The complete \(m\)-partite graph on \(n\) vertices in which each part has either \(\left\lfloor \frac{n}{m} \right\rfloor\) or \(\left\lceil \frac{n}{m} \right\rceil\) vertices is denoted by \(T_{n,m}\). The total vertex irregularity strength of some equitable complete \(m\)-partite graphs, namely, \(T_{m,m+1}\), \(T_{m,m+2}\), \(T_{m,2m}\), \(T_{m,2m+4}\), \(T_{3m-1}\) (\(m \geq 4\)), \(T_{n}\) (\(n = 3m+r\), \(r = 1, 2, \ldots, m-1\)), and equitable complete \(3\)-partite graphs have been studied in this paper.