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This note contains a plethora of counterexamples to attempts to generalizethe results of bi-parameter embedding from $p=2$ case to either $p>2$ or $p<2$.This is in striking difference to $p=2$ case that was fully understood in theseries of papers \cite{AMPS}, \cite{AMPVZ-K}, \cite{MPVZ1}, \cite{MPVZ2},\cite{AHMV}, \cite{MPV}. We also build a counterexample to small energymajorization on bi-tree. This counterexample shows that straightforwardgeneralizations of methods of \cite{AMPVZ-K}, \cite{MPVZ1}, \cite{MPVZ2},\cite{AHMV} from $2$-tree $T^2$ or $3$-tree $T^3$ to $4$-tree $T^4$ will notwork even for $p=2$ unless some new approach is invented.

Multi-parameter Carleson embeddings for $p\neq 2$ on $T^2$ or for $p=2$ on $T^4$, and why the proofs fail