Give it a try... open some files, start typing, it will offer completions from all files.
Assign hotkeys to items to insert one of the options (I have Alt-1, Alt-2, etc)
File types don't matter, this way completion works across python, python doctest, rst, txt
It's not codeintel, but try "variable.m", it shall offer "variable.method", space also works as a separator there, type: "Give " it will offer "Give it".
The options order is determined by "distance" from the current text position and recently used tab order.