This page from the website of a company that makes bio amplifiers
shows exactly how to do it.
www.biopac.com/AppNotes/ah206/wilson.htm

You set up the Wilson Central Terminal using jumpers and with 8
amplifiers, 10 electrodes, you can do the 12 lead measurement.
For example lead II can be derived from Leads I and III in software.
You can do the same thing with amplifiers from NI.
The note explains how to do the jumpering of cables reasonably well
and the software calculations required.
You would need to make up a Wilson Central Terminal lead.  I believe
the Wilson terminal has resistors in the branches.  Most texts on ECG
Instrumentation describe this.

There shouldn't be any disadvantage.  One thing to be careful of
depending on how the electrodes are connected is something called the
half cell potential.  This effectively creates a DC offset.  Many of
the DAQ cards are DC coupled and this makes it difficult to measure
the signal required within the dynamic range of the card.  This can
generally solved by AC coupling, which some cards have.  If not you
can make up a simple resistor & capacitor high pass filter.

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