When setting up a guitar for a player who uses many alternate tunings, my approach is a little different than normal setup work.
This is a great example of a simple question with a complex answer. A truly well-designed guitar setup often involves breaking down some of the finer details of action, neck relief, intonation, etc., and alternative setups can definitely screw up some of these fine adjustments. However, in most cases it is possible to find common ground. When setting up a guitar for a player who uses a lot of alternate tunings, my approach is a little different than normal setup work.
First, let's get started considering the size of the gap between the highest mood and the lowest mood. I rarely find alternative tunings with higher pitches or tensions than the standard E; The most popular alternatives involve, to some extent, lowering mood. Since one of the big benefits of the lower settings is the deep, rich bass register, I always like to adjust the settings to favor the lower tones when I can. This starts with string selection: for example, if a player regularly tunes the low E to C, I would recommend a thicker string that gives the low C some clarity and depth while still forgiving the standard E tuning. D'Addario's very useful online calculator for string tension and gauge was a great help to me.
Related: How To Tune a Guitar: Easy Beginner's Guide
A quick interlude: when changing string gauge strings, especially for larger models. Make sure the nut slots are cut correctly. A few thousandths of difference in diameter can make the difference between a saddle that adjusts smoothly and one that sticks and tightens: annoying in any context, but particularly problematic when trying to frequently switch from one setting to another. This is a routine task for any competent instrument technician and will always be a wise investment. Additionally, I have found that guitarists who tune frequently can wear out the nut grooves more quickly because the strings act as abrasives and eat away at the bone. In these situations, composite materials with self-lubricating properties are sometimes recommended (for example, Graph Tech Tusq products).
Once the string thicknesses are selected, they arise other complications. Attaching thicker strings to a guitar probably means you need to adjust the truss rod, and that's where the discussion begins. There is a significant difference (nearly 20%) in the overall tension of the standard tuning compared to something like the popular C G D G A D, and the ideal setup for these two tunings would require different truss rod positions. Also, setting it properly to a low tuning would probably provide a little more relief, as lower tension bass strings have more swing. Reality works against you here: without adjusting the truss rod between tunings, the highest tuning would have the most relief and the lowest tuning would have the least relief, so the opposite of what you want.
In these cases, I usually try to find a compromise between the lowest and highest tuning tension and position the truss rod at this medium tension. For example, if you use the settings above, you would ideally position the truss rod so that the guitar is tuned to D Ab D G Bb Eb, so that deviation from the ideal position in either direction is minimized.
Whenever possible, I also recommend guitarists look for hardneck guitars so they can play in alternate tunings. This not only minimizes variations in neck relief, but I and many other manufacturers have also found that neck stiffness can improve the response of low-frequency notes. The brilliant Adrian Legg, at the forefront of alternative tunings for decades, chose Adamas and other guitars with multi-piece laminate necks. Modern guitars with carbon fiber necks are also a good option.
The same tension problems also occur with the ceiling itself. On a lightly built guitar, the top may flex noticeably more at higher tunings than at lower tunings. Since there aren't many options available here, I'll use the same approach and set the bridge saddle height to a medium setting in hopes of keeping the upper and lower ranges close enough to the ideal setting to be satisfactory.
The final battle is intonation. It is reasonable to assume that a 0.052″ string tuned to E will have a different pitch point than a 0.058″ or 0.062″ string tuned to low C. Lower tension strings also tend to be less forgiving in this regard, as they are much easier to bend while playing. In some cases, musicians have brought me poorly tuned guitars, complaining of intonation problems, and the instrument has performed well with the electronic tuner, but the demands of playing real chords are very different from those of a controlled working environment.
Thicker strings tend to be less flexible and therefore require more pitch compensation. Since these adjustments on a guitar are often time-consuming and limited (after all, you can't get much out of a 1/8″ nut!), choosing string diameter can be a matter of choice. It's often a matter of finding a balance between the string that sounds best in low C and the one that sounds highest. Trying different string compositions (hexagonal core or round core and different core-to-winding ratios) can also help choose the best option, as can realizing that perfect intonation on any equal-tempered instrument is nearly unattainable and guitars are not an exception.
Alternative environments are a fascinating and exciting way to break away from conventional patterns and routines when practicing and composing. I can't ignore this issue without mentioning some key players who pioneered this approach: Joni Mitchell, Ani DiFranco, Pierre Bensusan, Will Ackerman, Andy McKee, Antoine Dufour, and many others have demonstrated the creative potential of alternative Moods. More recently, some adventurous musicians have incorporated tuning into the music itself; Jon Gomm and Alexandr Misko are excellent examples of the musical value of this technique.
With a few careful adjustments, most guitars can be tuned to improve the sound and feel of lower tunings, and the results can make all the difference you have to continue explore.