Let　G,H　be　graphs,　and　G⁎H　represent　a　specific　graph　product　of　G　and　H.　Define　im(G)　as　the　largest　t　for　which　G　contains　a　Kt-immersion.　Collins,　Heenehan,　and　McDonald　posed　the　question:　given　im(G)=t　and　im(H)=r,　how　large　can　im(G⁎H)　be?　They　conjectured　im(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　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.　©　2024　Elsevier　B.V.