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The importance of proper access to urban amenities for elderly residents is evidenced in the literature. Among them, mobility infrastructure, particularly public transport (PT), is of pivotal significance due to its intermediary role in access to other amenities such as healthcare or urban green space (UGS). Given this, the inequity in access to PT could lead to more adverse impacts on society, especially if it coincides with inequities in other amenities. In response, we calculate local indicators of spatial association (LISA) between the elderly population and urban amenities of PT, healthcare, and UGS at the suburban level of Melbourne Metropolitan. We, then, introduce and develop a LISA-on-LISA model to analyze and reveal the coexistence of inequities at the suburban level.  The results evidence the existence of inequity in access to PT for elderly cohorts. We further reveal the clusters of PT inequity which are, at the same time, experiencing healthcare and UGS inequities. The implications of the study for resource allocation and distribution in areas suffering from simultaneous inequity are discussed.