Duplicate records

I have a temporary membership database that has some duplication.  The problem is the on the effective and expiration dates.  They don’t match exactly but they fall inside the other records effective and expiration dates.  Here is an example:

Member_ID      Eff_Date      Exp_Date      Plan      Group
A1234567      1/1/2019      12/31/2019      110      AG569
A1234567      10/1/2019      10/31/2019      110      AG569

I there a way suing in sql to identify the duplicate inside the effective and expiration dates (2nd record) so that I could filter them out.  I don’t want to delete them, just be able to identify them.  Something like adding a field titled “Dups” that would have a “Y” in it if it is a duplicate.

The code for a simple query would be
SELECT Member_ID, Eff_Date, Exp_Date, Plan, Group
FROM Membership;

Thank,
Scott