This sounds like a job for the reaction roll!
If you drink a potion while still under the influence of another potion, most of the time the new effect cancels the previous effect. Similarly, if you mix two or more potions in a container, most of the time only one potion works and the others are canceled. However, roll a d6: on a 6, there's an unusual effect, determined by a follow-up 2d6 roll on the potion reaction table (use the 2d6 column on the mechanics-neutral table, or change it to a different dice roll on the same table.)
- Very High: one potion takes effect permanently. From now on, roll a d6 when drinking one potion; on a 6, use the potion reaction table again to see if the new potion interacts with the permanent effect.
- High: both potions take effect normally.
- Norm: both potions take effect, but the second potion lasts only 1d6/2 rounds.
- Low: the first potion's effect is canceled, the second potion has a random potion effect.
- Very Low: both potions are canceled, and there's a random harmful effect; either base it on a twisted version of one of the potions (Fire Resistance causes you to explode in flames, for example,) or roll as for a cursed scroll.