We report the data on-concurrent multiple point adsorption of two oppositely charged species of "target molecules" (aluminum ions and 1,3,6,8-pyrenetetrasulfonic sodium salt' (Py-4)) by a polyampholyte gel of N-isopropylacrylamide (NIPA, 6 M) with methacrylic acid (MAA, 80 mM) and methacrylamidopropyl trimethylammonium chloride(MAPTAC, 80 mM). The goal of this study is to test the mutual frustrations created by adsorption of one species on the adsorption of the other. Understanding these frustrations is an important step toward elucidating the memory of conformations in heteropolymer systems. We found that in the absence of aluminum, the adsorption of Py-4 was suppressed by gel collapse, presumably because of an increase in MAA/MAPTAC ionic pairs that prevents the formation of potential adsorbing centers. Adding a moderate amount of aluminum significantly enhances adsorption of Py-4 by the collapsed gel, indicating that aluminum ions compete for bonds with MAA and help release vacant MAPTAC centers. Finally, with further increase of aluminum, the Py-4 multiple point adsorption is again suppressed; pointing out the frustrations created by aluminum-mediated effective cross-links. We analyze also the cooperativity of the adsorption process.