I don't have any answers, just guesses and a couple of counter-questions:
I was going to guess that increasing the numbers of symbols in each character position increases the number of possible MRNs. However, even with just digits, 11 characters gives around 100 billion (10^9) numbers, which (IIRC) is larger than the estimates I'm acquainted with of the total number of humans who have lived or are living on this planet. If increasing the size of the pool is the reason, it would likely be planning ahead for something significant.
Another guess is that it might be to increase the pool to reduce the rate of adjacent numbers that are valid, sort of an error-detecting thing. If that's the reason, it would reduce the rate that a membership clerk looking up a member by MRN would have a digit or two wrong and have a valid number for a different person. That is somewhat plausible but still just a guess.
Is it only the last two character positions that have letters? Or, are the letters scattered around the rest of the columns?
Are all the letters A, B, C, D, E, or F? If so, that would indicate hexadecimal encoding. If there are other letters, that would indicate a more complex encoding scheme.