How do I dynamically add functions to a class and retain what the functions return in the class?

In my package, I have various functions (fun) that can interact with or modify stuff (for simplicity I use string fragments here), and return it. I now want to create a class that can collect what the functions return (Collector). I want those functions to become methods of the Collector class so that they can be called from its namespace - not directly though, but through a subclass which I call run.

So, when using collector.run.fun() I would like Collector to catch the output of fun so that it is available (in Collector's namespace) for further processing (e.g. by running more functions).

How do I dynamically add functions to a class and retain what they return in the class?

Here is some code. It's wrong, obviously - setattr will just attach fun to Collector.run...I don't know how to proceed though:

## package structure
## /my_pgk/module.py
## /my_pgk/sub/submodule.py

## many more like this in submodule.py:
def fun(add="default", **kwargs):
    if "base" in kwargs:
        add = kwargs.get("base") + " " + add 
    if "more" in kwargs:
        add = add + " " + kwargs.get("more")
    return add


## in module.py:
from sub import submodule

class Collector(object):
    def __init__(self, base, **kwargs):

        self.base = base
        if "more" in kwargs and not kwargs.get("more") == "":
            self.more = kwargs.get("more")

        class run(object):
            def __init__ (self):
                        
                ## dyanmically add class methods (this is wrong)
                for key, value in submodule.__dict__.items(): 
                    if callable(value) and not key.startswith('_'):    
                        setattr(self, key, value)                         
            
        self.run = run()     
        
        ## ENTER SOME PYTHON MAGIC HERE THAT ALLOWS ME TO RUN FUNCTIONS AS 
        ## CLASS METHODS AND CATCH THEIR OUTPUT FOR FURTHER PROCESSING:
            
        ## self.add = ...SOMEHOW CATCH METHOD OUTPUT...
        ## self.final = ", and ".join([self.base, self.add, self.more])
                
        
    def out(self):
        print(self.final)
    

## in practice:
col = Collector(base="(1) this is the start", 
          more="(3) even more is provided")
col.run.fun("(2) this is what I add")

col.out()
## should give 
# (1) this is the start, and (2) this is what I add, and (3) even more is provided