While some devices will work well with the address being switched while powered on, most datasheets will not reflect that. You will need to test it. To do that, you will need a few spare pins, or an extra 16 bit expander, to drive the address pins. A setup could be have the 13 led expanders A2 and A1 pins tied to logic high. A 14th expander, for driving the A0 pin, with A2, A1, and A0 tied to logic low (0x20). Every time you need to update a new expander, you update the address expander first, then the actual led expander. This adds a 2 to 3 byte i2c transaction to each update.
You have two main options for alternatives though. On the Arduino, you could use the software I2C library to have a second i2c bus. This can be on any two pins. Put 8 on one, 5 on the other.
Or for general i2c compatibility, a i2c multiplexer/hub/bus extender/repeater/switch (They have many names). Depending on the speed you are using (400kHz vs 1.7MHz [FM+]) you will need to find an appropriate one. Most are for 400kHz use. These allow you to connect two i2c buses, and switch between them.