There are different truss rods and truss rod neck designs and attachments.
Double action truss rod is a truss rod designed to bend one way when the nut is screwed one way and to bend the other way when the nut is screwed the other way. Single action truss rod is when the truss rod bends one way when the nut is screwed one way and gets released towards becoming straight (or initial position) when the nut is unscrewed.
Some manufacturers drill a canal across the neck and glue or temporarily glue the truss rod in the canal then some of them just mask the canal with the glued fingerboard on top, some may glue a stick into the canal permanently and then glue the fingerboard on top and some (hopefully the best) drill a hole through the neck rather than a canal to insert the rod there and the fingerboard is still glued but on the top of the real continuous wood of the neck. The last design allows for the rod to act on the hard wood neck in two directions. Good to have the hole in the middle.
Some manufacturers may leave the rod attached to the neck only and nowhere else. Thus the adjustment of the rod acts only upon the neck (hope not on the fingerboard) and not on the body nor the body neck assembly point. The advantage of this is to allow the rod to act only on the neck and not on the body thus preventing the rod from affecting the neck body assembly point. The disadvantage is the rod is not used to strengthen the neck body assembly point which point is either only glued or attached by wood screws or machine screws, washers and nuts, in some cases, with metallic plates.
A standard neck body assembly point in the fragile acoustic guitars may be to glue the neck to a wooden plank positioned inside the body with the side wood sandwiched in between. The rod goes through the neck and the wooden plank and the nut acts upon the plank as well as the neck. This way, the rod is used for neck strengthening/adjustment as well as, whenever possible, for neck body assembly strengthening. Obviously, in case of initial neck design to be slightly bent one way and to always require pressure by the always tightened nut and to provide for adjustment by exerting more or less pressure but always requiring pressure by the nut, the rod would also act as a support in the neck body assembly point.
Always study the rod and neck design of a given guitar to figure out what is best to do! Hope the manufacturers provide this information in the manual or on their web sites.
Too much pressure from the nut may break the neck body assembly point. The glue is very strong and wood has a good gluing property to allow the glue to penetrate into the bonding surfaces thus ensuring strength which may be greater than the strength of the wood, in other words, the wood would brake near the glued surfaces but the glued surfaces would remain glued. However: the more dense (tinier grain) the wood the less glue penetration. Ebony is harder than some metals and does not float on water but sinks in water. So huge density.
The truss rod better be used only for one purpose: not to allow the neck to bend after initial precision. This would require the manufacturers to do old school neck and bodies with huge tolerances as well as strong bodies and neck body assemblies and strong fingerboards not to allow neither the top wood nor the bottom nor the fingerboard to bend. The manufacturers would not be very happy this way though. They would rather do inexpensive woods and huge tolerances and leave to the customer to calibrate. Thus they prefer to use adjustable truss rods claiming also natural wood distortions with age. I would be happier in case the manufacturers were to make a very accurate neck and stick titanium alloys in the neck hole. Thus, the neck will never bend. May get swollen here and there with aging which can be corrected by sanding or gentle carving.
Therefore, in case you need a "normal" adjustment, use the truss rod. In case you need a bigger adjustment, do not overtight the nut! Do the things the old school: either bring the guitar to a guitar technician or evaluate where the biggest distance point of the curvature is (the centre point of the curvature) and apply pressure there by securing the guitar on a stand at the lower and higher points of the curvature and applying a counter pressure against the curvature. You can either steam the centre point of the curvature or blow hot air there.
Here is a dangerous home made solution: secure the guitar at the lowest and highest point of the curvature, for example, by putting these points on the backs of two cs and tighten these points with plastic tights. Then, put a rope with weights (not very heavy) at the centre point of the curvature: the point where the curvature is the most away of what the initial neck position is. Then either wait checking the curvature once in a while or attach a dryer to another c back or a microphone stand and point the centre of the jet to point to the 3D centre of the curvature (from the top). Blow hot air there but make sure you don't burn the wood or the paint/lacquer. Warm/hot water may also be poured towards the centre of the curvature but better be careful because the wood must fully dry before using otherwise will get bent again soon. Then leave this assembly for a while, checking very often not to over bent the neck in the opposite direction. Remember: manufacturers have the neck initially bent a bit or carved in a way to allow a bit more distance at higher positions. Don't overstrenghten the neck. Check the speck. Some manufacturers would suggest 2mm distance between the 6th thick E string and the 12th fret.
Once you bring the neck back to the initial shape, leave the neck for a while or check the neck when using. The neck may kick back towards the position before you tried to straighten. Wood has memory. You can reapply the process again but more gently than the first application.
Do not do this with expensive guitars. Not very accurate way. Unknown dependencies! Understand, the wood may not like neither too hot nor too much weight and the rope better be thin and strong. Metal wire with a cloth may be used. In case of an insolated metal wire, make sure you dont melt the insulation.
Another way would be to remove the fingerboard and sand or carve the neck to the initial shape. Or to remove the frets and carve/sand the fingerboard which can always be replaced with another one. Make sure the fingerboard is inexpensive. Another way would be to alter the height of the fret wire at different points. This may prove to be the least dangerous solution because the fret wires are supposed to be inexpensive and easily replaceable as long as you don't screw the grooves up.
The simplest way: remove the truss rod and the strings. Call a friend body builder, weight lifter, boxer, swimmer, navy seal, special forces, whatever. Tell the guy what you want to achieve to put a knee there and to pull. Make sure the guy understands and acknowledges the neck must not be broken nor the guy's hands or other parts enter the guitar body nor any other holes. Have the guy sweat a bit. Farting is desirable as long as in a direction toward the centre of the curvature. Keep warming the curvature in the already specified way with a dryer. This would make the guy sweat even more which is even better. Ensure no farts would project close to the electrical motor of the dryer because they may get ignited by possible sparks in the motor brushes. Keep checking how the strengthening goes very often. Wash well before using!
Again: Do not do this with expensive guitars. Not very accurate way. Unknown dependencies!