SQL Statement with multiple SETs and WHEREs

NO!

You'll need to handle those individually

Update [table]
Set ID = 111111259
WHERE ID = 2555

Update [table]
Set ID = 111111261
WHERE ID = 2724

--...

Best option is multiple updates.

Alternatively you can do the following but is NOT recommended:

UPDATE table
SET ID = CASE WHEN ID = 2555 THEN 111111259 
              WHEN ID = 2724 THEN 111111261
              WHEN ID = 2021 THEN 111111263
              WHEN ID = 2017 THEN 111111264
         END
WHERE ID IN (2555,2724,2021,2017)