When an observable is measured on an evolving coherent quantum system twice, the first measurement generally alters the statistics of the second one, which is known as measurement backaction. We introduce, and push to its theoretical and experimental limits, a novel method of backaction evasion, whereby entangled collective measurements are performed on several copies of the system. This method is inspired by a similar idea designed for the problem of measuring quantum work [Perarnau-Llobet et al., Phys. Rev. Lett. 118, 070601 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.070601]. By using entanglement as a resource, we show that the backaction can be extremely suppressed compared to all previous schemes. Importantly, the backaction can be eliminated in highly coherent processes.