When it comes to more than three top-level tabs in Android you can consider using a navigation drawer as Facebook for Android App uses.
Android Guidelines show this example about the navigation drawer:
The user can open the drawer panel by touching the navigation drawer
In this case the "navigation drawer indicator" is placed on the left of the screen.
In Facebook for Android App the same indicator is on the right, which I think is a better solution since about 90 percent of the population is right-handed:
In my opinion the potential advantages of a navigation drawer are:
- If the "navigation drawer indicator" is placed on the right of the screen as on Facebook for Android, the options displayed are closer to the user's thumb. Since new, additional options are placed from top to bottom, they they get closer and closer as the number of options increases.
- A navigation drawer is vertically scrollable, so potentially you can display many options (as on Facebook for Android App) and they'll still be very legible/usable.
- The navigation drawer is an Android standard pattern and it's also used in Facebook App, so we can assume many users are already familiar with that (it may or may not be true to your app's target users).
The potential disadvantages of a navigation drawer are:
- Not every user is familiary with the navigation drawer pattern.
- The "navigation drawer indicator" is not a standard icon, su users might miss it.
- Options contained in the drawer are not immediately visible, while in the top-tab the first 3 options are immediately visible.