You can add some baking soda to regular shampoo to make it fight grease better. Put some shampoo in your palm, add some baking soda and mix it up well (it's an abrasive when dry, but fine when disolved).
Also, I second (third?) the vinegar rinse or lemon juice rinse suggestions. Just be sure to dilute it to about 1:7 to 1:9 (one part vinegar or lemon juice and seven to nine parts water). At that strength, it will help the hair shafts to seal well (which helps scalp oil move down the hair, which helps the hair near the scalp stay less oily), AND it will help gently remove excess oil. If the solution is stronger, it can cause bounce-back oiliness - it will strip the hair, and then the scalp tries double hard to replace the oil.
Vinegar or lemon juice rinse is a leave-in conditioner - don't rinse it out.
(By the way, white vinegar or lemon juice is better for oily hair than apple cider vinegar. ACV has "solids" that, while really good for dry or damaged hair, can cause hair that is oily-to-normal to appear over-conditioned.)
I discovered vinegar rinse as a teen with oily hair. It's great, even if you keep using commercial products. I've used it as the final rinse for my hair for about 30 years, making the solution weaker as I aged and my hair became less oily.