How can I execute a group of commands as another user in Bash?

Try this:

su somebody <<'EOF'
command1 -p 'parameter with "quotes" inline'
command2 -p 'parameter with "quotes" inline'
command3 -p 'parameter with "quotes" inline'
EOF

<< introduces a here-doc. The next token is the delimiter, and everything up to a line beginning with the delimiter is fed as standard input to the command. Putting the delimiter in single quotes prevents variable substitution within the here-doc.