Extended Kalman filter gain
Ok, so the question is not "Can the Kalman gain be bigger than 1?" but "Can the Kalman gain for this system be bigger than 1?"

In that case, I suggest you look at the evolution of the Kalman gain given your system and see if there are any conditions where it does. Perhaps for this particular system it can't be. You'll need to specify all the parameters of your signal model to do that.



Of course it's possible!

Why do you think the KF gain is less than 1? What the Kalman gain is depends on the system model and the data being processed.

There are plenty of examples showing gains greater than 1. See, for example, the image below taken from here.