Hi, I just completed the mission All Hands on Deck as well as the Ice Cream and Printing Press missions. How do unlock more story mode missions?

buy the Malibu club

If you've done the print works, than I assume you've completed the storyline and the final credits have rolled. There may be a few properties still to buy - The malibu club has a load of missions with it, the film studios on Prawn Island has missions. There's also the Sunshine Autos car dealership where you steal cars listed on a board, and also get access to street races for cash. The boatyard is for sale, giving you a boat course to run against the clock, Pole Position club can be bought - you have to go into a booth and watch a dancer for 10 mins or so to get a cash pickup outside. Have you done all the rampages? What about the Cuban cafe, Haitian, biker and Love Fist missions? You probably have but you never know. If you can't find anything, send me your saved game and I'll have a look for you. Always willing to help

If he's not done "Keep Your Friends Close.." then he's not finished the story, you need to own 5 (I think its 5) properties in order to trigger the final missions.