>> 0. emacs -Q
>> 1. Type these two lines:
>> str 1
>> str 2
>> 2. On the third line type:
>>  s                      ;; self-insert-command
>>  M-/                    ;; dabbrev-expand
>>  SPC                    ;; self-insert-command
>>  C-M-/                  ;; dabbrev-completion
>>
>> This correctly displays all available completions
>> “str 1” and “str 2”.  But ‘s M-/ SPC M-/ M-/’ doesn't get
>> the second completion.
>
> ’s M-/ SPC M-/’ doesn’t do a normal completion, it does this (from 
> the manual):
>
>     After you have expanded a dynamic abbrev, you can copy additional
>     words that follow the expansion in its original context. Simply type
>     <SPC> M-/ for each additional word you want to copy. The spacing and
>     punctuation between words is copied along with the words.

Oh, this special-casing unfortunately breaks the natural workflow.

> I suppose that subsequent M-/’s are undocumented, but the current
> behaviour is, IMO, definitely confusing as it seems to search other
> buffers for completions even though there are valid completions in the
> current buffer.

Maybe it's possible to break out of the vicious cycle of ‘SPC M-/’
repetitions by making ‘SPC M-/’ look like a normal expansion, e.g.: