These are some of the songs, date wise, according to BJ.com that were written at between 1996-1999 that may have been included:

THESE ARMS ARE OPEN ALL NIGHT (Unreleased demo circa 1998 recorded with the Big Dogs in New Jersey.)
I GET A RUSH (Unreleased demo circa 1996.) Recorded in New Jersey.
SOMEDAY JUST MIGHT BE TONIGHT (Unreleased demo circa 1996.) Recorded in New Jersey.
GARAGELAND (Unreleased demo from 1999.) Recorded in New Jersey.
MAYBE SOMEDAY (Unreleased demo from 1999.) Recorded in New Jersey.
LAST CHANCE TRAIN (Unreleased demo from circa 1998.) Recorded in Los Angeles with Aerosmith's Joe Perry on guitar.
RICH MAN LIVING IN A POOR MAN'S HOUSE (Unreleased demo from 1998.) Recorded in New Jersey and Los Angeles with Dave Stewart.
ONE THAT GOT AWAY (Unreleased demo from 1999.) Recorded in New Jersey.
YOU CAN SLEEP WHILE I DREAM (Unreleased demo circa 1999.) Recorded in New Jersey.
SHUT UP AND KISS ME (Unreleased demo from 1997.) Recorded in New Jersey with the Big Dogs.
CRAZY LOVE (Unreleased demo from 1998.) Recorded in Los Angeles and New Jersey.
ORDINARY PEOPLE (Previously released b-side from 2000's CRUSH album.) Recorded in New Jersey.
SATELLITE (Unreleased demo from 1999.) Recorded in New Jersey.
REAL LIFE (Movie soundtrack from 1999's EDTV.) Recorded in New York City (at Avatar Studios, which had originally been the Power Station where Jon Bon Jovi had started his music career as a gofer) and New Jersey. It was remixed for inclusion in the box set.
TOO MUCH OF A GOOD THING
(Unreleased demo from 1999 prior to CRUSH album.) Recorded in New Jersey.
RIVER RUNS DRY (Unreleased demo from 1996.) Recorded in New Jersey.
KIDNAP AN ANGEL (Unreleased demo from 1999.) Recorded in New Jersey.
TEMPTATION (Int'l b-side from CRUSH album in 2000.) Recorded in New Jersey.
ALL I WANNA DO IS YOU (Unreleased demo from 1997.) Recorded in New Jersey.

On top of that there are other B sides on the singles from Crush.

Looking at some of these songs I feel there could have been a much stronger overall album.