The paper explores the consistency of metric-affine gravity, a theory that generalizes Einstein's General Relativity by allowing for independent affine connections. The authors introduce an extended projective (EP) symmetry, generated by a pair of vectors, which is more restrictive than the known projective symmetry. They prove that the most general EP-invariant theory, composed of quadratic operators, is free from pathologies such as ghost and strong coupling problems. This theory includes a massless graviton and a single additional scalar field, suitable for inflation. The model also contains effective 4-Fermi interactions capable of producing fermionic dark matter. Additionally, the authors discuss an alternative double-vector symmetry, iso-Weyl (IW) invariance, which leads to a healthy theory with a propagating vector field. The EP symmetry is derived from the non-minimal coupling of fermions to the geometry, highlighting the role of fermions in gravity. The paper concludes by suggesting that EP invariance is as relevant to metric-affine gravity as diffeomorphism invariance is to the metric formulation of General Relativity.The paper explores the consistency of metric-affine gravity, a theory that generalizes Einstein's General Relativity by allowing for independent affine connections. The authors introduce an extended projective (EP) symmetry, generated by a pair of vectors, which is more restrictive than the known projective symmetry. They prove that the most general EP-invariant theory, composed of quadratic operators, is free from pathologies such as ghost and strong coupling problems. This theory includes a massless graviton and a single additional scalar field, suitable for inflation. The model also contains effective 4-Fermi interactions capable of producing fermionic dark matter. Additionally, the authors discuss an alternative double-vector symmetry, iso-Weyl (IW) invariance, which leads to a healthy theory with a propagating vector field. The EP symmetry is derived from the non-minimal coupling of fermions to the geometry, highlighting the role of fermions in gravity. The paper concludes by suggesting that EP invariance is as relevant to metric-affine gravity as diffeomorphism invariance is to the metric formulation of General Relativity.