There are 2 titles associated with this firm.

Piozzi , H.L.T. (1789). Observations and reflections made in the course of a journey through france, italy, and germany. by hester lynch piozzi. Dublin: Patrick Wogan [23 Old Bridge] James Moore [Dublin] William Jones I [Dame Street] Thomas Heery. Patrick Byrne I [Grafton Street] Bernard Dornin [College Green] Hannah Chamberlaine. Luke White [Dame Street] Grueber and McAllister.
Howard , I. (1790). Thoughts in the form of maxims addressed to young ladies, on their first establishment in the world. by the countess dowager of carlisle. Dublin: James Moore [Dublin] William Jones I [Dame Street] Hannah Chamberlaine. George Draper. John Jones [Grafton Street] R. White [Dublin] Grueber and McAllister.