gnu grep multiple filters in one regex

RHEL 8, if it matters.

I need to find all the rows in a text file which match these three filters:

cut -f1 -d: .pgpass | grep ^FISP | grep -E 'CDS|TAP' | grep PGS401
FISPCDSPGS401A
FISPCDSPGS401B
FISPTAPPGS401AA
FISPTAPPGS401AB
FISPTAPPGS401BA
FISPTAPPGS401BB
FISPTAPPGS401CA
FISPTAPPGS401CB
FISPTAPPGS401DA
FISPTAPPGS401DB

This, similar to bash’s extended globbing, is the kind of command I’m looking for, but doesn’t match.

cut -f1 -d: .pgpass | grep '^FISP@(CDS|TAP)PGS401'
cut -f1 -d: .pgpass | grep -E '^FISP@(CDS|TAP)PGS401'

What’s the secret sauce?