Topological conjugation classes of tightly transitive subgroups of $text{Homeo}_{+}(mathbb{S}^1)$

Let $text{Homeo}_{+}(mathbb{S}^1)$ denote the group of orientation preserving homeomorphisms of the circle $mathbb{S}^1$. A subgroup $G$ of $text{Homeo}_{+}(mathbb{S}^1)$ is tightly transitive if it is topologically transitive and no subgroup $H$ of $G$ with $[G: H]=infty$ has this property; is almost minimal if it has at most countably many nontransitive points. In the paper, we determine all the topological conjugation classes of tightly transitive and almost minimal subgroups of $text{Homeo}_{+}(mathbb{S}^1)$ which are isomorphic to $mathbb{Z}^n$ for any integer $ngeq 2$.