It's not unusual to have an aircraft with a dozen add on STC's (or more) and who is approving all this - the AME installing them? Believe me, I ARE ONE. No one is watching what is going
Every MAE who signs on an STC, signs for the following - it's right on every certificate:
Prior to incorporating this modification, the installer shall establish that the interrelationship between this change and any other modification(s) incorporated will not adversely affect the airworthiness of the modified product.
That requirement, in the context of Standard 571, Appendix A:
(d) Performance and Flight Characteristics
Does the modification or repair involve alterations that:
(1) significantly increase drag or exceed aerodynamic smoothness limits?
(2) significantly alter thrust or power output?
(3) affect stability or controllability?
(4) induce flutter or vibration?
(5) affect the stall characteristics?
Means that the AME is responsible, as always, for having the data which says that two (or more) otherwise unrelated STC's are compatible. In the absence of that data, the AME must obtain it, most commonly by seeking a serialized STC for the plane, which links the STC's to each other. I have done many sSTC's which do nothing other than approve STC'd mods together on one plane. My record was a 182, from plain Jane to amohib with 27 STC'd mods combined. Nearly 30 hours of development and flight testing, including taking a TC Test Pilot for his evaluation of some of the mods.
A few years back I was asked to approve an AoA system on a C 206H with other wing mods. In doing the flight testing, and following the installation instructions for the AoA system, I found an unsafe condition. After consultation with the AoA manufacturer, I offset a set point for the AoA, and the plane was entirely safe. I issued the sSTC, and then reported what I'd learned to TC. 5.5 hours of set up and test flying to make a safe, and approvable plane.
Yes, combining mods can result in unintended characteristics, Owners are being responsible by having the whole job done properly, including the research, and possible approval of multi mods. AME's are being thorough when they assure that they have the data for the mods they are doing/combining. Pilots are being responsible when they are assuring that their operations, and external loads that they might carry are within the approved limitations for the plane.
If in doubt, stop and ask - which is the opening theme of this thread....
As for the accident I was in, I was PNF, finishing a float rating for a skilled pilot, in ideal conditions. Something went wrong, and I can report that I simply do not recall what. I remember going from looking out to the right, thinking, we're going to touch..... now... and we touched nicely, to waking up in hospital four days later. Only lesson learned, when right seat PNF, look forward during landings, not out to the side, no matter how confident you are about the skill of the other pilot!