On the 3rd floor on my house in Marikina City I have grown, Potatoes, Carrots, Onions,
Pumpkin (nearly took over the whole area ) and tomatoes. All were grown in bags. Not grow bags but the much bigger specialised bags. Everything was OK but I need to water/Shade/tend everyday , which is OK for me as I love to grow.
It can be done even in Manila, as steve says you might be very suprised.