Preventing pre-mature shell parameter expansion in chained commands - bash

Question

I have a system that allows commands to be executed from a host to various external machines, from a bash shell script using either ssh or 'sersh', which is similar to ssh but sends commands over a serial port. (The details of these commands don't matter.)
I'm trying to chain the commands together, from one external machine to
yet a 3rd machine. I'm having a hard time figuring out how to get the shell to expand parameters only on the final machine.
function do_cmd () {
case $TRANSPORT in
ssh)
ssh -i ${SSH_KEY} ${LOGIN}#${IPADDR} "$#"
;;
serial)
sersh ${SER_LOGIN}#{SERIAL_DEV} "$#"
;;
ssh2serial)
ssh -i ${SSH_KEY} ${LOGIN}#{IPADDR} \
"sersh ${SER_LOGIN}#${SERIAL_DEV} $#"
;;
*)
echo "Unknown transport $TRANSPORT"
;;
esac
}
do_cmd "echo hello"
do_cmd "echo \"my pid is \$\$\""
do_cmd "cd /proc ; for pid in 1* ; do echo \$pid, ; done"
All three of these calls work correctly when TRANSPORT is 'ssh' or 'serial'. For the TRANSPORT 'ssh2serial', in the second call to do_cmd, the $$ is expanded prematurely (on the intermediate machine, not on the final machine). And for the third call to do_cmd, $pid ends up
being expanded to the empty string before the loop executes on the
final machine.
I thought about double-escaping the dollar signs, but the
caller doesn't know how many levels of intermediate machines there are.
Is there a way to prevent the parameter expansion on the intermediate
machine, and only do it on the final machine?

Answer 1

[#MadPhysicist reminds me that I'd still have to escape the variable expansions. My answer is left here below for reference but #MadPhysicist is right: my answer probably fails to answer the question asked.]
Use eval.
Try this exercise, typing the following four commands at your shell's command line. I believe that the exercise is likely to answer your question.
$ X=55
$ A='echo $(( $X + $X ))'
$ echo "$A"
$ eval "$A"
Once the exercise has shown you what the shell's built-in command eval does, you can get the effect you want by using eval on the final machine in your chain.
[Please notice that the exercise says, A='echo $(( $X + $X ))'. It does not say, A=`echo $(( $X + $X ))`. Observe the way the quotation marks slant. You want ordinary single quotes here, not backticks.]