Parametric Marcinkiewicz integral on grand variable Herz-Morrey spaces

We establish the boundedness of the parametric Marcinkiewicz integral ${\mu }_{\mathrm{\Omega }}^{\rho }$ and its higher-order commutators $[{\mathrm{\Lambda }}^m,{\mu }_{\mathrm{\Omega }}^{\rho }]$ with $\mathrm{B}\mathrm{M}\mathrm{O}$ symbols on grand variable Herz-Morrey spaces $M{\dot{K}}_{\lambda ,\beta (\cdot )}^{\alpha (\cdot ),\gamma ),\theta }({\mathbb{R}}^n)$. These results also apply to grand variable Herz spaces, including the case where $\alpha (\cdot )$ is constant.