Hi Sioxie!
I use LightWave to do what you're asking about.
I've never seen Max (I'm on a Mac,) but I'm assuming the general technique would be similar.
First, I remap the Avatar. I make a new Texture map, and give it a new name (what I call it depends on what I plan to do with the map. Tights, for instance, need different mapping than Hawaiian shirts, or pajamas, or striped sweaters. If the collar or cuffs need their own maps, I name them something meaningful so I can remember what it was for.) Then I order the UVs so that they will do what I need them to do.
Each material gets its own layer in the Modeler file (one for Upper body, one for Lower body, one for Head if it's going to be used, and so on.) I also put some polys into selection groups, for instance, the Back or the Front, which includes polys from all three Materials.
Usually, I add an additional layer for the Sleeves, and one for any extra parts. For instance, for a shirt I might make a couple extra layers to hold the upper and lower material, and offset them slightly so I can make a shirt that doesn't quite match in the center front. (Where there would be a seam in RL, but isn't one in SL.

)
I also typically map the polys around the neck separately, so that I can make a seamless collar in the finished garment.
Since each layer will get its own image when they are burned, I just arrange things to make sure that there will be no overlap at that stage, using as many maps and models as it takes to get what I want.
As I set up each map, I set the Surface for that group of Polys to use it, so I can see what I'm doing when I'm ordering the UVs. (For more on that process, you can check the tutorials on my site. I'll put a link at the bottom of this post, since the code has been turned off, and the addy is quite long.)
Once all that is done, (and it can take a while so you might want to reuse them if you can,) I go into the Surface dialog, and choose the Image that will be shown on them all. This is the Fabric, and works exactly the way that real fabric would, if you were cutting a garment from it.
Usually, I use a seamless texture from Photoshop, sized to 1024x1024, so if the UVs project off the "0 to 1" UV Map, the wrapped image will remain seamless. That gives me the freedom to scale the vertices on the map, so I can get the size I want for the texture on the Avatar.
When I have it the way I want it, I take it from Modeler to LightWave (the Render portion of the package,) and Bake the texture from my own UVs to the Linden Avatar UV Map. (Baking is one of the things that differs quite a bit from app to app. Check the documents for yours to see if and how it bakes. I know that Max does. I'm not sure about Blender or some of the others.)
As mentioned above, each section gets its own image, so for instance, I might have one baked image that is the Sleeve pattern, one that's the right upper, one for the left upper, one for the right lower, one for the left lower, and one for the collar.
Once that's done, I take the various baked images, which are now split up onto the Linden maps, and assemble them into the garment I want in PS. That's where I add all the details, shadows, wrinkles, and so on; because I find that there's less distortion if I just draw it than there is if I try to bake the shadows and things on.
Of course, I'm rarely designing clothing for women, so your milage may vary.

(Most of my stuff is either Unisex or for kids.)
This is not the only way, of course, but yeah, that's how I get the textures to flow seamlessly around the arms, across the Upper and Lower jacket portions, and around the legs for tights.
That being said, you still have to have a seam someplace, because of the way the mesh itself is built. I just choose to have them where the seams are on a real garment.
For things like a t-shirt, where the entire body is a tube in RL, without any seams, I take the mesh into Modo, and paint over those seams to match the texture. This is much more time intensive than remapping; which takes a lot of time to make the map, but very little for new "fabrics", but it gives a really nice effect, and if you plan your fabric carefully it's not difficult.
The other way to do that is to make a set of UVs that has the seam in the back, for instance, and then you can retouch in PS itself.
Anyway, that's how I do it.

Hope this helps!
The addy for the UV Mapping tutorials is
http://www.robinwood.com/Catalog/Technical/LightwaveTuts/LWPages/LWUVStart.htmlMind you, all of that is old now. I wrote it for LW 7.5, and LW is now in version 9. Mapping and UV Unwrapping tools are much better now than they were then. But the same general principals apply, if you're ordering the UVs by hand.