Here is a step by step thing, though I'm sure Flare or someone else will end up posting pictures which I can't do atm.
Open the data editor.
Select Unit tab.
Right click desired unit.
Go down to Duplicate Unit
Check all the actors of the unit(or just the model actor)
click okay.
At this point if you duplicated a marine another one will appear right next to the original.
One text is a light green the other is the usualy color
select the right green one
right click
select modify
change the name field(and field under if you wish)
That gets you a duplicate unit with the same stats as the original. Now if you want to start changing things you need to make your own behaviors,effects,abilities and then link those to your unit.
well the most important one to have checked to get the model is the actor withe the unit model. You might be running into the fact that when ever you duplicate this actor for some reason the actor doesn't change to the correct file path. SO what you can do is change your thing from all data, to just your map data and go to actors
find the model you wanted and then change the name of the unit the actor works for to your unit.
unfortunately I can't make images since I'm not at home atm. I will look around and see if I can find any already posted though, might be back for an edit
If you want to just reference the unit to what the original is go to Data -> Add Object
Fill in the fields and at the bottom option select Copy From and select the unit you want it to be like in the drop down list.
Now if you are duplicating the unit and you find it turns out to be a sphere go to the model part of the unit and make sure it's set correctly. Duplicating a model can add a "2" to the end of the model path making it incorrect.
Ghan has said he has fixed this. Monovertex please confirm this fix. This was only a problem with people that had signatures in the upper levels like not the special members but the respected members.