Double and triple Givental's J-functions for stable quotients invariants

We use mirror formulas for the stable quotients analogue of Givental's Jfunction for twisted projective invariants obtained in a previous paper to obtain mirror formulas for the analogues of the double and triple Givental's J-functions (with descendants at all marked points) in this setting. We then observe that the genus-0 stable quotients invariants need not satisfy the divisor, string, or dilaton relations of the Gromov-Witten theory, but they do possess the integrality properties of the genus-0 three-point Gromov-Witten invariants of Calabi-Yau manifolds. We also relate the stable quotients invariants to the BPS counts arising in Gromov-Witten theory and obtain mirror formulas for certain twisted Hurwitz numbers.