Multiple parallel IIR bandpass filters with different centre frequencies combined into one filter for optimisation... possible?
So, what I took away from my multirate lectures is: 

You don't use IIRs in that case, because the recursive part isn't shareable among multiple filter implementations (being specific to the output of each filter), and hence, you end up with a lot more multipliers than you'd have if you went for a FIR system and removed redundancies. This is especially true for hardware/FPGA implementation, where placing a wire to use a result twice is cheap. You're doing software, so saving a few registers worth of filter taps really won't pay -- you're breaking the linear nature of memory access that way, and that will impose a performance hit that is much, much worse.

In fact, I'd challenge you to look at how you can understand your filter bank as an array of filterbanks with identical filters.

For example, assume that all your BPFs have equally spaced center frequencies $\frac{f_\text{sample}}{N}$. Also, they might have different bandwidths, but since you say they are related to each other, let's assume there's one "maximum bandwidth" that is a multiple of all smaller bandwidths.

Now, implementing a polyphase filterbank ("channelizer") with a BPF of that maximum bandwidth and the constant frequency spacing is very efficient. Basically, it's like taking a single very BPF at full rate, add one FFT, and you get the complexity of the system for up to $N$ channels (note: this is $N-1$ free channels!). Then, take the channels whose bandwidth you'd need to be reduced further. Now, assume these $m&lt;N$ channels all need to be reduced in bandwidth by a factor of $4$, for example. So that's $m$ identical quarterband lowpass filters! Implementing identical filters in hardware is pretty efficient, usually, especially because after the first filterbank, sampling rate might already be reduced (so you can multiplex multipliers); now, you're seemingly doing audio on a PC: 

Take these $m$ channels, and just implement individual filters. There's nothing much you can or need to optimize here; assuming this is on something that has a PC-like CPU, caching will keep your filter taps close to CPU registers, and and only the actual samples will need to go through memory buses. Also, not that things like $\frac{1}{M}$ low pass filters are relatively relaxed in transition width requirements, and hence, FIR implementations are short in taps, and thus fast.

As usual in signal processing, decimate whenever possible! The polyphase filterbank might already decimate, but also your $m$ channel low pass filters should do that, too, and in a clever manner (a polyphase lowpass decimator runs at the output, not the input sampling rate!). Not processing samples you don't need is probably reason Nr. 1 that modern DSP is so capable.