Are there any air defense systems that initially fire with radar tracking and switch to infrared tracking once they get close to target?

I hear that stealth aircraft are not undetectable to radar but radar not detectable enough for an accurate target lock. If you could launch a missile in the general direction and then use infrared guidance once you got close enough, you might be able to shoot down stealth aircraft. There is a limit to how much you can hide heat from an aircraft due to thermodynamics. You would need a rather large infrared scanning sensor on the missile. The other idea I had was launch 2 missiles simultaneously, one acting as the actual interceptor and the other having a radar to guide the interceptor, kind of like a mini AWACs.