I have found that while AssociateTo will not work, AppendTo will.
Halyomorpha halys ?
In[6]:= (* This does work *)
AppendTo[as[["summary"]], "stuff" -> "someStuff"]
Out[6]= <|"stuff" -> "someStuff"|>
In[7]:= as
Out[7]= <|"name" -> "myName", "summary" -> <|"stuff" -> "someStuff"|>|
>