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It is fundamental that you need to do your attenuation before any peaking filters, and also ensure that you don't break 0dB at any point in the filter chain.Perhaps more easily: When doing these things you need extra headroom, upping your dynamic range requirements. Even playback volume normalization (i.e. ReplayGain) counts. Here I'm attenuating a bunch of material to around -15 dBFS peak tops, since RG preamp is set fairly low. That's 2.5 more bits that are technically needed. Of course that's relatively loud material that doesn't exactly make use of most of the 16 bits to begin with, but still.
But typically this is done by using 56 bit floating point or 32 bit fixed point for all the internal DSP calculations. For example a MiniDSP flex will take your 44.1/16 input, convert it to 96/32 itself, do all the work, then output analog signal. All you have to do is remember to use the built-in attenuation of the MiniDSP to make enough headroom for the rest of your filters. Upsampling to 96/24 before you hand it to the MiniDSP isn't going to hurt, but it's not adding anything either.
If for some specific reason you do need to attenuate 16 bit content before putting the signal into the DSP pipeline then converting to 24 bit before attenuation is of course the only way to do it without loss of info. I'm curious what ReplayGain software you are using that doesn't do all this automatically?