Bash: save both stdout and stderr separately, whilst printing stderr.

save_stdouterr_print_err.sh

# https://stackoverflow.com/questions/9112979/pipe-stdout-and-stderr-to-two-different-processes-in-shell-script
# Executes the command, prints the errors, and save the stdout and stderr as separate files.
save_stdouterr_print_err () {
	commandstr="$1"
	stdoutpath="$2"
	stderrpath="$3"
	if [[ $# -lt 4 ]]
	then
		SSH_EVAL='eval'
	else
		SSH_EVAL="$4"
	fi

	{ { { eval "$commandstr" 2>&1 1>&3; } | $SSH_EVAL "cat | tee -a '$stderrpath'"; } 3>&1 1>&2; } | $SSH_EVAL "cat >> '$stdoutpath'"

}

# Example
# Notice real-time changes. Rather than waiting until the command finishes, it actually writes on the fly.
# 1. Save locally (a.txt and b.txt)
save_stdouterr_print_err '{ echo a; sleep 5; echo >&2 b; sleep 5; echo a; sleep 5; echo >&2 b; }' a.txt b.txt 
# 2. Save to ssh server (sv:~/a.txt and sv:~/b.txt)
save_stdouterr_print_err '{ echo a; sleep 5; echo >&2 b; sleep 5; echo a; sleep 5; echo >&2 b; }' a.txt b.txt 'ssh sv'