Quite simply, you need an audio interface with a minimum of 8 inputs. If the inputs
include mic pre's then you can get that mixer out of the way, which would be preferable
IMO.
There are plenty of options. SOS recently did a round-up of multi-channel
interfaces
HERE.
The older RME Fireface (not the UFX) is still my favourite at this time, for it's
price, hassle-free drivers, TotalMix software and audio quality.
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An Eagle for an Emperor, A Kestrel for a Knave.