The super-strong conjecture on F-irregular graphs

Let $n\geqslant 3$ be an integer. A graph $G$ is $n$-hyper-irregular if it is $F$-irregular for every graph $F$, not necessarily connected, with order $|F|\leqslant n$ and size $|E(F)|\geqslant 2$.

Super-strong conjecture on $F$-irregular graphs. For each integer $n\geqslant 3$, there exist infinitely many $n$-hyper-irregular graphs.

This is presented as a conjectural strengthening of the preceding $F$-irregularity conjecture. The supplied text gives no resolution or partial result for this super-strong version.