The pilot-in-command (PIC) reported that, nothing abnormal with the tailwheel-equipped airplane occurred during initial taxi, takeoff, or during the approach. During the landing, after touchdown, as power was reduced and the airplane began to “settle”, the airplane veered right. He attempted to correct for the veer, added engine power, and the airplane became airborne. During the second flight around the pattern the safety pilot (SP) flew the airplane and the approach with no issues. The SP performed the second landing, and after the touchdown the airplane veered to the right again. The SP and PIC attempted to correct for the veer to no avail. The airplane subsequently continued to veer right, exited the runway on the right side, impacted a snowbank, and came to rest inverted. The airplane sustained substantial damage to the left wing and empennage. The PIC reported that the nature and circumstances of the incident caused him to believe that there was something mechanical that forced the airplane to turn rapidly to the right during both landings. However, the PIC did not know what that could be. The airplane had a wheel alignment performed the day before the accident, and the airplane was taxi tested with an additional two takeoffs and landings with the airplane “tracking satisfactory”, before being signed-off. A post-accident examination of the airplane by a Federal Aviation Administration inspector revealed no mechanical failures or malfunctions. It was noted that the alignment of the main landing gear and wheel could not be determined due to the amount of side-load the airplane experienced during the accident.