The Selhurst Park club have already broken their transfer record this summer and their co-chairman says that their business is not yet finished.
Parish also accepts that this season will be a huge step up for the club, who have never enjoyed a Premier League campaign without being relegated.
"We are excited, and nervous. It's a massive step up, everybody knows that," Parish told Sky Sports News.
"We're determined to give it a good shot, so, along with developing the stadium, we're looking at the squad.
"We're not where we want to be just yet. I'd like three or four at least before the weekend closes, maybe even four or five.
"We need the right characters. We know where we want to be but we have never survived in the Premier League. We need players that are going to fight and die for the cause."
Crystal Palace are involved in the first Super Sunday game of the season when they take on Tottenham Hotspur in the lunchtime kick-off.