EMB-175 Captain reported numerous equipment failures while enroute and resulting in a diversion.

Narrative

Aircraft X ZZZ to ZZZ1 Divert to ZZZ2We were flying along at FL340 when the master caution went off and I called identify cancel. ADS1 fail; spoiler fault; tat 1 fail; and Speed Break fail. In night IMC headed into weather. We started to run QRH procedures which led us to turn off the auto pilot and descend out of RVSM. We also lost both flight directors; both flight path vectors and LNAV would intermittently fail and revert to roll mode but auto pilot was not engaged. We called for vectors and lower altitudes and worked to complete all QRH. It seemed the trim was running slower than normal. This led me to believe there might be other systems affected as non of the QRH procedures stated to expect the trim to run slower or to lose your flight director or FPV. I haven't even seen the FPV fail in the sim. We notified the Flight Attendant's and then the Pax that we were going to divert to ZZZ2. I requested priority handling because we were uncertain of the root of the problem and if it would get worse and if there was anything else effected. We had to burn gas so not to not land over weight. We set up for a long straight in visual approach to ZZZ2 with a FLAP FULL landing as per the QRH. We got and addition 8 EICAS messages on the ground on taxi in and even more on parking. Maintenance met the plane. While headed to ZZZ2 we had some potential course and altitude deviations of up to 400 ft. The flight was completed safely. I called Dispatch and then Scheduling.