Yes! I can and have painted interlocking monograms from other designers than Shuler Studio. You must check with who designed yours and provide written proof that I am allowed to paint that design in watercolor. 

If the triple monogram has the letters side-by-side (like in my TWD), I paint the first name initials the same and then the surname in contrast from those two letters. If the letters are stacked, centered on top of one another, using three shades of the same color works best. For a couple with someone having two first names, each person gets their own contrast just as if it was two letters.

When you order a monogram from Shuler Studio, they make the groom's letter darker by shading it with stripes. I paint each letter completely, so for solid vs. stripes, the bride may end up being striped because that is the lighter of the two once painted. The general rule of thumb is that the bride is the lighter letter.
However, the other element I factor in is the thickness of the letter. If the bride's letter is thinner, then she will be the darker of the two. Otherwise, the design won't be balanced.
If you're stuck between using solid vs. stripes or light vs. dark, envision how you'll use this monogram on its own. For crest design, I normally suggest light vs. dark because it draws your eye to the center and tends to be more simple. 

My watercolor monograms are painted once to replicate the original design. They do not come with edits. If you change your mind about color or contrast, you would need to pay for a new painted monogram.