bash multiple heredocs et al

In this case you could consider using bash with its -s argument:

sudo -u buildmaster bash -s -- "$PARAMETER" <<'END'# do all sorts of crazy stuff here including using variables, like:ARGS=somethingARGS="$ARGS or other"# and so forthPARAMETER=$1END

(note that you have a syntax error, your closing END is quoted and shouldn't be).

There's another possibility (so that you have lots of options—and this one might be the simplest, if it applies) is to have your variables exported, and use the -E switch to sudo that exports the environment, e.g.,

export PARAMETERsudo -E -u buildmaster bash <<'EOF'# do all sorts of crazy stuff here including using variables, like:ARGS=somethingARGS="$ARGS or other"# and so forth# you can use PARAMETER here, it's fine!EOF

Along these lines, if you don't want to export everything, you may use env as follows:

sudo -u buildmaster env PARAMETER="$PARAMETER" bash <<'EOF'# do all sorts of crazy stuff here including using variables, like:ARGS=somethingARGS="$ARGS or other"# and so forth# you can use PARAMETER here, it's fine!EOF

Substituted your quoted prefix into your unquoted full document:

# store the quoted part in a variableprefix=$(cat <<'END'ARGS=somethingARGS="$ARGS or other"END)# use that variable in building the full documentsudo -u buildmaster bash <<END$prefix...END