Enter the Voltcraft LZG-1 / Extech CT40!
With this gizmo, you can trace up to 16 wires at once. The system uses a remote unit with 17 alligator clips (16 + one for the common/return conductor).
The remote unit sends a 5V pulse width modulated “square” wave to the main unit. Clip 1 is a ~52% duty cycle wave, and Clip 16 is about 98% duty cycle – at 32 Hz. This allows the main unit to distinguish between each wire reliably – as long as the resistance of each wire is less than 30kohms (which is pretty high).
The main unit also doubles as a DMM. Although it’s not the greatest digitial multimeter, it’s good enough for most applications.