  This note contains a plethora of counterexamples to attempts to generalize
the 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 the
series of papers \cite{AMPS}, \cite{AMPVZ-K}, \cite{MPVZ1}, \cite{MPVZ2},
\cite{AHMV}, \cite{MPV}. We also build a counterexample to small energy
majorization on bi-tree. This counterexample shows that straightforward
generalizations 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 not
work even for $p=2$ unless some new approach is invented.
