What's the maximum number of outputs you can control from a microcontroller with n outputs?
It depends on what you mean by "control". Are you confining yourself to simple combinatorial logic, or are serial protocols allowed?

In theory, you could control an arbitrary number of outputs from a single pin by using something like the Dallas/Maxim 1-wire (serial) protocol to drive a set of I/O expander chips. Similar approaches can be used with I2C, SPI, or simple shift registers, each of which would require a minimum of 2 pins.