Based on my understanding, I don't think there is any particularly compelling evidence that there is an entirely new layer beneath what we know. But it's always a possibility. For example, it wouldn't be too surprising if modern physics breaks down beneath the Planck scale (equivalently, at very high energies) [1], or inside black holes.
In other words, I think both the possibility that we are nearing a complete understanding of the rules and the possibility that we are nowhere close are both quite plausible.