Sure there are. The theory has been tested within only a teeny tiny part of the range of its predictions. For example it predicts gravitational redshift in the range of 0% (no redshift) to 100% (black hole), but experiments to date have shown a maximum gravitational redshift less than 0.01%. It matters less how many tests of GR are done than how extensively those tests cover the range of what GR predicts.
While we have little experimental data to definitively show that GR is the correct theory of gravity, we do know that it leads to major problems for physics, like its breakdown at gravitational singularities, its incompatibility with quantum mechanics, and the black hole information loss paradox. A competing theory of gravity that is confirmed by all experimental tests of GR to date need not have any of those problems, indicating that a lot more testing of GR is warranted.