There are MIRV-killer warheads too, Falcon. Like the American Multi-Object Kill Vehicle, designed to fit an SM-3 interceptor. This is an older version. The new version is still classified:
Penetration aids like kilometer long chaff spools, decoy or dummy warheads, Mylar balloons, radar jammers... they're all tried and test methods and they work, but they aren't fool proof and advanced intercepts have the means to discriminate between live warheads and dummies via various metrics such as heat, weight or filling.
That said, most interceptors designed to knock out MIRV missiles try to do so before separation, to make an interception and total destruction of the missile easier and more complete. GBI tries to do this at ranges upwards of 3000km and beyond.
MIRVs and MaRVs, as found on the retired Pershing II:
Complicate the process, but don't make the missile infallible either. There are countermeasures and tactics available to a nation to defeat MIRVs.