Hi Slapin.
There are 2 ways of doing this.
Old Way (proxies):
Copy the blend file you want to link (Eg – My_rig.blend and My_rig_01.blend)
And then link in each copy separately.
(yes that is annoying but it used to be the only way)
New Way (Library Overrides):
Link in the asset. Then create a Library Override for it. If you have the file organised into collections (before the linking), this will create that same structure in your working file. Then you can just duplicate the whole linked collection as many times as you need.
(each copy will be appended with a .001 or .002 which really bugs me – but there’s nothing I can do about that)
The key in both situations is to have your asset (rig) in a structured collection, then you link in that top level collection that pulls everything into your file.
Hope that helps.