Yes you can make your hair more oily if you wash your hair too much.
When you wash your hair too much you can irritate the scalp and cause more excess oil to be produced which can cause your hair to become more oily.
Washing your hair too often causes you to strip your hair of natural oils and when that happens your hair goes into oil production and then your hair gets too oily as a result.
Using too much hair shampoo or hair conditioner can also cause greasy hair due to buildup.
Washing your hair every few days or once per week is usually enough to keep your hair healthy and clean and if you do need to wash your hair more often you should use a moisturizing shampoo and moisturizing conditioner.