As noted in the "disclaimers" in the manuals mentioned here, published guidance does not cover every possible scenario. It is not required to cover any scenario considered extremely remote (less than one in 10.000.000 hours), and most independent dual failure scenarios are extremely remote. Any single failure with multiple effects (like hydraulics taking out half your brakes, some spoilers and a reverser) will be covered in the manual.
That said, you can apply some engineering knowledge to make your "good judgment" as good as it can be:
For conditions where the multiple factors are related to the same deceleration mechanism, you probably want to multiply the factors. Example: I have one pair of brakes failed and 2 of 8 spoilers inoperative. Lets say the factors are respectively 1.6 and 1.2 for those conditions. Since the spoilers are used to dump lift, the spoiler failure is making the remaining brakes less effective (i.e. the two failures interact). So in this you could use 1.6 * 1.2 = 1.92 as a factor (unless the manual contains other guidance for this condition).
Same would apply to brakes+contaminated runway, since both are related to your ability to decelerate via friction.
For conditions where the factors are unrelated, you can probably just add the factors (excluding the base landing distance - more on that in a minute). Example: I have one pair of brakes failed and the left thrust reverser failed (bear with me here, I know T/R generally does not go into performance, so you would not need a factor). Lets say for the purpose of this example you have factors of 1.6 and 1.1 respectively for these conditions. In this case you could use 1+(1.6-1)+(1.1-1) = 1.7, where the whole +1 -1 nonsense is to account for the fact that a factor of 1.6 is 60% additional runway, and a factor of 1.1 is 10% additional runway and we are trying to add the required additional runway length, since we don't expect the reverser failure and the brake failure to have any significant effect.
Next, anything affecting your energy state (say, increased approach speed because your flaps are stuck) should be handled multiplicatively (like the first example) with any other factor. The higher energy interacts with any and all of your deceleration features - so if any of those are failed the effects will be cumulative.
Last but not least, always keep in mind that energy has a quadratic relationship with speed (i.e. is proportional to the square of your speed), while most deceleration features (everything except aerodynamic drag) are linear in nature (i.e. they reduce your energy at a constant rate). So a 10% reduction in deceleration does NOT mean a 10% increase in landing distance. It is more. A 20% increase in approach speed does NOT mean a 20% increase in landing distance. It is more.
And finally, all of this is mostly moot. If you are dealing with multiple independent failures affecting your deceleration capability you should land at the longest available runway within reach regardless (unless that means a long diversion and you have reason to land ASAP, like a fire on board).
: This information is provided for educational purposes only. Don't sue me if you have an overrun!