Let　G,　H　be　graphs,　and　G　*　H　represent　a　specific　graph　product　of　G　and　H　.　Define　im(G)　(　G　)　as　the　largest　t　for　which　G　contains　a　Kt　t-immersion.　Collins,　Heenehan,　and　McDonald　posed　the　question:　given　im(G)　(　G　)　=　t　and　im(H)　(　H　)　=　r　,　how　large　can　im(G　(　G　*　H)　)　be?　They　conjectured　im(G　(　G　*　H)　)　＞=　tr　when　*　denotes　the　strong　product.　In　this　note,　we　affirm　that　the　conjecture　holds　for　graphs　with　certain　immersions,　in　particular　when　H　contains　Kr　r　as　a　subgraph.　As　a　consequence　we　also　get　an　alternative　argument　for　a　result　of　Guyer　and　McDonald,　showing　that　the　line　graphs　of　constant-multiplicity　multigraphs　satisfy　the　conjecture　originally　proposed　by　Abu-Khzam　and　Langston.　(c)　2024　Elsevier　B.V.　All　rights　are　reserved,　including　those　for　text　and　data　mining,　AI　training,　and　similar　technologies.