> Would it be possible to make the A-156 to accept negative voltages too

Not in an easy way. The A-156 was developed as an expansion module for the
A-155 which outputs only positive voltages. As the AD converter of the A-156
accepts only positive voltages you need an additional offset that shifts the
negative voltage into the positive range. One of the mixers A-138a/b/c, the
A-129-3 or the new precision adder A-185-2 can be used to obtain such a
positive offset.

Best wishes
Dieter Doepfer