As a reward for reaching the last-four last term, USP are entering at the second round stage and face a trip to Combined Counties League Premier South side Frimley Green on Saturday.
Former manager Glenn Turnbull might have moved to Moneyfields while just a few of the squad who were part of that incredible run to the semi-finals, which ended in penalties heartache at the hands of Binfield in May, remain at the Victory Stadium.
And despite admitting it'll be ‘extremely hard’ to repeat those historic FA Vase achievements from last season, Grice is refusing to rule anything out.
He said: ‘We’re going to look to progress because we know firsthand what it can do in terms of revenue, but more importantly for the profile of the club as well.
‘Last season I was still involved in the first team with Glenn and I would be doing the Twitter at times and stuff like that.
‘When we played on the Saturdays (in the FA Vase), you’d look at the amount of followers we had after each game, it would go up and up.
‘Good exposure is good, we want to improve the image of the club, we want to attract better players to the club and what better way to do that then going on a decent run.
‘You never say never (embarking on another memorable run) and we’ll give it our best shot.
‘Let’s make no bones about it, it’ll be extremely hard to replicate what happened last season.’
US Portsmouth have been dealt the blow of losing loanee Lamin Jatta who, after netting twice in five outings for Grice's men, has been recalled by parent club and Wessex League Premier Division rivals AFC Portchester.
Midfielder Tom Dinsmore is cup-tied for the trip to Frimley having featured for previous club Portchester in the competition earlier this season.
Long-term absentee Frankie Paige is continuing to make good progress from a recurring hamstring issue but will not be fit in time for Saturday’s FA Vase trip.