SQL Copy set - 'clone' with FK updates

I need to copy a set of data that has parentID as a field... so when I take a set of existing records and insert them, I'll need their parentID to REFLECT the NEW PK - not the old one.

I'm curious if there is a SQL way to do this - currently I'm doing a bunch of logic @ the application layer and updating the records - so I'm storing the OLD recordset, and doing a lookup based on old ID, old parent ID...

heck - maybe there is a 'clone' or 'copy & update FK' - I'm using MySQL 5

a dataset may look like this

+--------+---------+------+
| ID(pk) | PID(FK) | NAME |
+--------+---------+------+
|  3123  |    0    | Bob  |
+--------+---------+------+
|  3127  |    0    | Jim  |
+--------+---------+------+ 
|  3400  |  3123   | Sue  |
+--------+---------+------+
|  3123  |    0    | Rik  |
+--------+---------+------+
|  3127  |  3400   | Cara |
+--------+---------+------+
|  3400  |  3400   | Pat  |
+--------+---------+------+

So the copied records might take on these IDs -where the PIDs in () are the unknown values that I need to know HOW to derive. they cannot be presumed to be sequential or singular.

+--------+---------+------+
| ID(pk) | PID(FK) | NAME |
+--------+---------+------+
|  4000  |    0    | Bob  |
+--------+---------+------+
|  4001  |    0    | Jim  |
+--------+---------+------+
|  4002  | (4000)  | Sue  |
+--------+---------+------+
|  4003  |    0    | Rik  |
+--------+---------+------+
|  4004  | (400开发者_如何学Go2)  | Cara |
+--------+---------+------+
|  4005  | (4002)  | Pat  | 
+--------+---------+------+