Yes, if you use a high enough MOI, you'll start to get double infections. Usually, anything >1 MOI will guarantee a high chance of double infections. If you're using a high MOI and only seeing single inserts, it might be due to your cells being difficult to transfect. If you look at this site: https://manuals.cellecta.com/lentiviral-construct-packaging-and-transduction/v10a/en/topic/lentiviral-titer-calculation it should give you a general reference for what % double transfected cells you should see. The difference between transfected cells and MOI % should estimate double infections assuming 100% efficiency.
Some cells are less efficient at being transfected, and it's a good idea to get a functional titer on your target cell line which is very easy if you have a fluorophore in the plasmid you're trying to insert.
I reread what you're getting at, and it's generally accepted that MOI under 0.4 won't give you double transfections.