You can have both when the cutter stay is fairly close to the jib stay. First of all, Google
"twin head sails
and setups and designs" to see how old timers did this; before the advent of cruising spins, this was the preferred downwind option in the trades.
It's fallen from favour due to the fiddliness, cost and effort involved in having twin poles out, but once set, you can go literally for days in some areas without touching a line.
Back to having "both": It's possible to have a) twin head stays with two hanks, b) twin foils with matching sails and poles, or c) poled out port on jib stay and poled out starboard on staysail stay, or vice-versa.
Obviously, you'd want a reduced head sail the same area as the staysail for balance. That might involve a separately hoisted sail on the jib, or a partially furled sail. Depends on the boat and the sail, but other cutter owners and your sailmaker
A cutter is versatile and safer in some respect for the short-handed cruiser as you can bail on the powerful jib when the wind
rises and stay farther inboard in sail handling and sail effort. A cutter-rigged ketch
might be the best option, but we aren't talking about that here.
A lot of cruisers until the 1990s used this technique and many still swear by it. For me, I will have the ability to do this, because it'll allow me to have a lot of power when it's too blowy to run an assymetrical cruising chute (above, say, 15 knots). The cruising chute is easier to handle, but won't stand up to higher winds or partial, cycling collapses as the wind is blanketed by following waves higher than the stern, leaving you with the option to bag it and fly twins up to the mid-20s in true wind speed.
With a 41 footer (same as me), you want all the options you can afford in sail handling over distances, I feel. Stuff rips, stuff breaks. Doesn't mean you can't keep going!