playing off previous runs?
You can not add tiles vertically like a crossword(number) puzzle. If a set has 4 or more tiles you can move one of them to create a new set. As long as the remaining sets are valid.

For example if 3,4,5,6 is on the table and you have two 6 (all three of different color) you can move the 6 and create a new set with your two 6 tiles. Getting 3,4,5 and 6,6,6.