Minimal surfaces in the three-sphere by desingularizing intersecting Clifford tori

For each integer $k \geq 2$, we apply gluing methods to construct sequences of minimal surfaces embedded in the round $3$-sphere. We produce two types sequences, all desingularizing collections intersecting Clifford tori. Sequences first type converge a collection $k$ tori with maximal symmetry along these circles. Near circles, after rescaling, smoothly on compact subsets Karcher-Scherk tower order $k$. second desingularize same supplemented by an additional torus equidistant from original circles intersection, so that latter orthogonally intersects former pair disjoint orthogonal near which corresponding rescaled singly periodic Scherk surface. The simpler examples resemble constructed Choe and Soret \cite{CS} different where number handles circle is same. There plethora new are more complicated for differs. Examples as well.