How to connect phototransistors in an additive style? The output current should resemble the total power of light received by all of them. Eg. if one gets 0 lux, the other one 10 lux, the result should be "10", likewise if both of them getting 5 lux. Is there a simple solution like a phototransistor - resistor - network?
Sounds like all you need is basic current summing. This can be as easy as connecting them all to the same resistor.
The current thru a phototransistor is largely independent of the voltage accross it, so the voltage on the single resistor won't effect the individual currents. To be clear, connect all the photoresistors in parallel between a power supply and this resistor. The other end of the resistor goes to ground. The voltage accross the resistor will be proportional to the sum of all the phototransistor currents.
Chose the resistor based on the maximum brightness all the phototransistors would experience that you care to measure. Let's say each photoresistor allows 1mA to flow under whatever your maximum light conditions are, and that you have 8 such phototransistors connected in parallel. That means the maximum current thru the resistor would be 8mA. Let's say you want that to result in a 0 to 3.3V signal, and the phototransistors are connected to a 10V supply. 3.3V / 8mA = 413 Ohms, so chose the next common size down so that you still have a little headroom at max brightness.
Look at the datasheet of the phototransistors carefully to see what the actual current will be, not just the 1mA I picked out of the air. Photodiodes usually only allow uA to flow, but with a phototransistor there is gain and only the datasheet can tell you what that is. It's also a good idea to do some experiments with your intended light conditions since humans are rather bad at guessing light levels. Make sure that with maximum light there is still enough voltage accross the transistors for them to operate in roughly the constant current region.
For an application combining multiple phototransistors pointing in different directions to expand the field of view, greater sensitivity was had with separate resistors to ground on each detector, with the junctions joined through diodes, such as 1N4148, to a common resistor to ground. Higher voltages appear on the common output despite the diodes cutting voltage 1/2V because the unstimulated detectors do not drain current from the active one and divide the output voltage. This especially applies to oscillating emitter detection increasing the amplitude of the output voltage oscillations. These can be filtered with capacitive coupling to an op amp for amplification. Without the diodes I was not getting much of a signal when more than one detector merely shared a common resistor.
For photodiodes instead of transistors (required for higher frequency comm such as tv remotes) I did not find the same difference and a common resistor seems correct.