general relativity - How close can two extremal black holes with the same charge can get?

Here's a puzzle I have been pondering over.

If we have two extremal black holes with the same charge, the electrostatic repulsion between them ought to cancel the gravitational attraction between them. Without any net attraction or repulsion between them, how close can we bring these two black holes to each other without merging? A peculiarity of the metric seems to suggest the event horizon is always infinitely far away for extremal black holes $\int_R^r dr' \frac{1}{r'-R} = \infty$. Does this give enough elbow room for both black holes to get arbitrarily close to each other without merging?