at some point in time

Your question has three parts:
1. How many meanings do

At one point in time,

and

At some point in time,

have?
2. What is the meaning of

every member of the group had a fight with every other member of the group.

?
3. If I combine

At one point in time,

or

At some point in time,

with

every member of the group had a fight

with

every other member of the group.

how many possible meanings could I express?

You have placed the most important phrase at the beginning of the sentence and thus nobody knows what

At one/some point in time,

qualifies

4.

(i) At one/some point in time,

can qualify either ‘had a fight’ or ‘every member of the group’ ->

every membe

r of the group

, a

t one/some point in time,

had a fight…

/

every member of the group had a fight

at one/some point in time …

You will see these have separate meanings.

5.

At one point in time,

= at a specific time that (a) I have referred to (b) that I will refer to (c) that we do not know

6.

At some point in time,

= (i) at an unknown time. (ii) at an unimportant/not significant time.

You may wish to compare the use of

At one/some point in time,

with the use of ‘only‘:

Only I lent you a watch.
I only lent you a watch.
I lent only you a watch.
I lent you only a watch.