Reference Coin Boosts Capacity

Exactly one coin among a pile is counterfeit, with weight different from the genuine ones, but you do NOT know whether it is heavier or lighter. You also have ONE extra coin that is guaranteed genuine, which you may place on the scale freely. Using a two-pan balance (each weighing returns left-heavy, right-heavy, or balanced) with exactly 3 weighings, what is the LARGEST number of suspect coins for which you can always both identify the fake and determine its direction? Weighings may be adaptive.