Over the course of two months we have had 3 different customers deposit fraudulent checks that are all drawn on John Doe's closed account at another Bank. There is no link between our 3 customers except that they all deposited checks from John Doe's closed account.

-SAR #1 on the first situation (customer A), our knowledge was that our customer was a victim and John Doe was the suspect.
-SAR #2 when we discovered the second situation (customer B) we filed a separate SAR and noted the first SAR in the narrative. Our knowledge was that our customer was a suspect and so was John Doe.
-We now have a third situation with customer C and need to file. Our knowledge for the third situation is that our customer and John Doe are suspects.

Because all 3 situations involve John Doe's account at another Bank, would we be better off to file an amended SAR to combine all 3 situations into a single SAR, or continue to file separately for each of our affected customers and note previous SAR's in the narrative?

I wouldn't file an amended SAR when nothing has changed on those reports simply for the purpose of combining. I wouldn't file #3 now either, in fact. I would consider it additional activity on SAR #1 and file it in 90 days from that SAR, adding all suspects you have (and at that time discuss that you are combining in SAR #2).

However, I WOULD add all items to the local police report as they happen so they can get after John Doe.

you could be dealing with a ring that has chosen you as the lucky bank of the week.

I would close all prior to dealing with the SAR issue.

If they did not deposit the checks you could open a new one.

While it's possible that the three customers have never heard of one another, there is definitely a link between them: They all dealt with or are in cahoots with the fraudster. Talk to them. Try to connect the dots.

There is no guidance on "combining" SARs based on a common theme song, just opinions, of which this is only one. After talking to all three customers, I would file a SAR identifying the two previous SARs and telling a condensed version of their stories and a full version of this story noting all common denominators; i.e. I would combine the 3 instances into a single SAR and say that I had done so.