I just set up my tarp in 20mph wind with gusts up to 35mph. I'm using a top ridgeline with prusik knots and taught line hitches. I ended up ditching the tie-outs and just directly staked the tarp to the ground. Would adding a bottom ridgeline additionally to the top shelf reinforce the tarp? It did not feel like it would survive much higher wind.

Ideally, I would like to withstand 40mph winds with various tarp setups. I mainly carry this tarp for shelter if anything happens to my tent.

Add some shock cord to your tie out lines, that will give you some mechanical advantage with the wind. Just tie off a circle of it at your attachment points, then your line to the circle then to the stake. Makes a big difference.

Shock cord definitely helps. Other than that - quality of the tarp material and workmanship is the limit that one can't reinforce.
Also, I'd make a ridgeline tighter. Taught line hitches do not survive strong wind, while trucker's hitch will. To take the stress off the ridgeline tie-outs, I keep the ridgeline under the tarp, not above it. Another useful option in high winds are tie-outs in the middle of side panels, two on each side (like on this picture ). Tying them to trees on both sides of the tarp makes the set-up more wind-proof, but this feature could be difficult to add, depending on the tarp's material.

Add another 'ridge line half way down the tarp. Also double stake the bottom and/or tie off to a tree base/log/roots and possibly double-guy out the stakes.

pd

I think you need different tarp. I use Cliff Jacobson method for wind. The tarp in pic is 10 x 12 with 10 running along ridgeline. 10 x 14 or 12 x 12 would work great too. I use 9mm (I am guessing) climbing rope for ridgeline. I only bowtie the attachment points on the ridgeline with the exception of the two outside ones which I wrap around 7 or so times before I tie the simple bowtie. I then stake out the bottom of the tarp to the ground. I usually use different stakes but that is all I had on this trip. You need to then tie out the middle or put a pole in it like I did. I use nesting pole vs shockcorded one since I can leave out sections to make it the right length. After that you tie line on ridgeline to ground (in pic I had tree in front so I tied to tree). That will keep the wind from bobbing tarp up and down. You might have to blow up my pic to see these lines. You then run line on each side of tarp to the ground (in the middle).

Lots of tarps (tents too) shaped like that will have additional tie-outs in the middle of the 'wall' - the big, wind-catching side needs additional support in center.

That is something you could add pretty easily with the most basic of sewing skills.