Can the output of a BIBO stable positive feedback system grow more than its input?

[Simactricals]

I am using an IIR filter which is a second order system which has zeros and poles such that the system is asymptotically stable.
The passband gain of the filter is unity.
The input range to the filter is [4,-4].
Will the output ever exceed the limits of the input due to the positive feedback in the discrete system even though the system is completely stable?