How to parallel two voltage signals
The simplest (for some folk) will be to use a small MCU with a couple of ADC inputs and a DAC output then you can use the power of the MCU to do what you want by comparing digital representations of the signal levels.

But this method (and a straight analogue-ish) method raises questions such as: -


How accurate do you want the output level to be?
How accurate do you want the input signal testing mechanism to be?
What speed or frequency might the inputs be changing at?


If you were to use an analogue method I would make three circuits that: -


Produced the positive maximum (using op-amp precision rectifers) output
Produced the negative maximum (using op-amp precision rectifers) output
Produced the sum and then precision rectified the output to get only a positive result


I would then make three circuits that tested each scenario (using comparators) and, with additional steering logic, I would enable analogue switches to select one of the three outputs I wanted to be my final output.