The most common and most likely answer to this crossword clue is the 4 plus 3 letter word PLUS ONE
I've seen this crossword clue in The Guardian
P
L
U
S
O
N
E
Buddy explains!
The straight part
We know that "It says you can invite any partner along" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it says you can invite any partner along = plus one.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PLUS ONE mean?
PLUS ONE noun- A friend or date whom one brings along to an event; a guest of a guest.