Question

How can you get more room to put items in your secret base?

Answer 1

You can get more room to put items in your secret base capturing people's flags from their secret base in Diamond, Pearl and Platinum. Here's a list

You haven't stolen any flags yet.
Number of items you can have in your base:10

You've captured 1 flag.
Number of items you can have in your base:12

You've captured 3 flags.
Number of items you can have in your base:15

You've captured 10 flags.
Number of items you can have in your base:15(Still)

You've captured 50 flags.
Number of items you can have in your base:15(Same)

Answer 2

You can steal another player's secret flag from THEIR secret base and you can break the rocks in your base. You can also move your secret base to another place by buying those drills items from Hikers.