A trekking AKA butterfly bar will offer more hand positions and let you reuse your current controls.
Or put some drop bar ends on your flat bar.
Either keep all controls where they are, or add a pair of drop bar brake levers appropriate for your brakes. Some shimming may be required.
Do note that a shorter stem is often needed with drop bars to keep the reach about the same.
Full system rebuilds are possible, but may require more substitutions.