The technical reason for getting more credit cards (AND PAYING THEM OFF AS YOU GO) is that it will improve your "utilization ratio", which is A) the amount of your AVAILABLE credit compared to the ACTUAL credit you are presently using. You need to increase your overall "credit line" in order to improve your utilization ratio.
B) This comes under the category of "Amounts owed" when calculating your FICO score (Fair Isaac) - This category is fully 30% of the total determination in arriving at your score, only exceeded by "Payment History" which is 35% of the determination of your FICO score.
Contrast that with the fact that the opening and/or non-opening of new credit cards only weighs 10% in that score determination, coupled with the fact that the opening is a short-term hit, whereas the utilization ratio is a long-term positive IF YOU KEEP THE RATIO FAVORABLE by PAYING AS YOU go, this ostensibly counter-intuitive method works well for folks with credit problems that are on a path to improve them.
Don't go crazy, and as I said before, it IS important to USE the cards, as you will see the fastest rise in your score, improved offers from other creditors, etc.
I would re-visit my existing credit cards once better offers arrive---as in getting rid of the old ones--- UNSOLICITED ones, btw. You'll know the good offers when you see them.