Penn State last won the Big Ten Tournament in 2015.
The announcement came after Parker decommitted freom West Virginia on Monday.
Israel-Achumba joined safety King Mack, wide receiver Malik McClain, and running backs London Montgomery and David Kency Jr. in the portal.
This was McClain's second time entering the portal after transferring to Penn State last year.
Kency became one of five Nittany Lions to hit the portal Thursday.
Montgomery joined a slew of other Nittany Lions to hit the portal on Thursday.