This paper presents three multivariable generalizations of a matrix inversion result derived from Bailey's very-well-poised $ _{6}\psi_{6} $ summation formula. The original result, presented in [24], involves two infinite matrices that are not lower-triangular and is directly extracted from an instance of Bailey's $ _{6}\psi_{6} $ summation. The authors derive three multidimensional extensions of this result using Gustafson's $ A_{r} $ and $ C_{r} $ extensions of the $ _{6}\psi_{6} $ summation, as well as the author's recent $ A_{r} $ extension of Bailey's $ _{6}\psi_{6} $ summation. These new multidimensional matrix inverses are then combined with $ A_{r} $ and $ D_{r} $ extensions of Jackson's $ _{8}\phi_{7} $ summation theorem to derive three balanced very-well-poised $ _{8}\psi_{8} $ summation theorems associated with the root systems $ A_{r} $ and $ C_{r} $. The paper also includes several multivariable extensions of basic hypergeometric series, including $ A_{r} $, $ C_{r} $, and $ D_{r} $ extensions of Jackson's $ _{8}\phi_{7} $ and Bailey's $ _{6}\psi_{6} $ summation formulas. The authors provide detailed proofs of these results, including the derivation of three multidimensional matrix inverses and their applications to the derivation of balanced very-well-poised $ _{8}\psi_{8} $ summations. The paper concludes with a discussion of the implications of these results for the theory of basic hypergeometric series and the potential for further generalizations.This paper presents three multivariable generalizations of a matrix inversion result derived from Bailey's very-well-poised $ _{6}\psi_{6} $ summation formula. The original result, presented in [24], involves two infinite matrices that are not lower-triangular and is directly extracted from an instance of Bailey's $ _{6}\psi_{6} $ summation. The authors derive three multidimensional extensions of this result using Gustafson's $ A_{r} $ and $ C_{r} $ extensions of the $ _{6}\psi_{6} $ summation, as well as the author's recent $ A_{r} $ extension of Bailey's $ _{6}\psi_{6} $ summation. These new multidimensional matrix inverses are then combined with $ A_{r} $ and $ D_{r} $ extensions of Jackson's $ _{8}\phi_{7} $ summation theorem to derive three balanced very-well-poised $ _{8}\psi_{8} $ summation theorems associated with the root systems $ A_{r} $ and $ C_{r} $. The paper also includes several multivariable extensions of basic hypergeometric series, including $ A_{r} $, $ C_{r} $, and $ D_{r} $ extensions of Jackson's $ _{8}\phi_{7} $ and Bailey's $ _{6}\psi_{6} $ summation formulas. The authors provide detailed proofs of these results, including the derivation of three multidimensional matrix inverses and their applications to the derivation of balanced very-well-poised $ _{8}\psi_{8} $ summations. The paper concludes with a discussion of the implications of these results for the theory of basic hypergeometric series and the potential for further generalizations.