Unfortunately, in Ohio, DUI offenses are never expungable and would make you ineligible for expungement of any other offense on your record. Pursuant to 2953.36(B), a conviction for a violation under chapter 4511 (DUI) or a substantially similar municipal ordinance, is ineligible for expungement.
Regardless, a common misconception is that you can expunge an offense when you have more than one offense on your record. You must be a "first offender" to be eligible for expungement. "“First offender” means anyone who has been convicted of an offense in this state or any other jurisdiction and who previously or subsequently has not been convicted of the same or a different offense in this state or any other jurisdiction." There is a limited exception: "when two or more convictions result from or are connected with the same act or result from offenses committed at the same time, they shall be counted as one conviction."
Basic rule: if the offense is eligible, you get one bite at the apple, when there is only one apple on the tree, and there haven't been any apples on the tree in the past.