Quite a lot. There was the mentioned perihelion procession. There was the Michelson-Morley experiment demonstrating a constant value for speed of light regardless of the relative motion of the source and detector. There were measurements of gravitational redshift of gamma rays in earth based buildings (gamma rays showing lower frequency after traveling up from the ground to the roof). Theee is experimentally measured time dilation using extremely accurate atomic clocks (one flown around the earth several times showing less passage of time by a few microseconds). There is the observed distribution of muon energies from cosmic rays. Based on their resting half-lives we should never observe muons at ground level, but we do because of time dilation, with fewer high energy ones decaying. Then there are GPS systems which only work accurately if we adjust the clocks in them based on general relativity. Finally there is the Eddington expedition that made Einstein famous. Einstein predicted that the apparent position of stars near the sun would be different from their position when not near it because curved space in the sun’s vicinity would cause light to travel a curved path. This was not observable during a total eclipse, which Edfington and his team measured confirming Einstein’s prediction. There may be others that I am unaware of, but relativity has passed all experimental tests and is not seriously questioned
An entangled particle in a distant galaxy instantaneously moving a particle here on this thread would "amend" special relativity wouldn't it?