Due to its simple design additional banks of memory can be added very easily to the TR606, and thanks to the way the memory is accessed the banks can be made switchable in realtime so you can cut between rhythms on the fly. Further, with modern SRAM devices it is possible to keep the data backed up by a small lithium battery for decades.
Big + Easy
The magic that makes all this possible to do cheaply and (more importantly) internally to the 606 is the DS1258Y NVSRAM from Maxim.
The original pair of 1k x 4 SRAM devices in the 606 (IC7 and IC8) share almost all of their signals except for the active low chip enable (CE) and the address line on pin 15. From IC6 we can prove that both chips are never selected at the same time so its simply a matter of multiplexing the two differing address lines by one of the chip select signals. A simple multiplexer assembled from a 4011 quad NAND gate is show below.
Once you have a multiplexer combining the two address lines of pins 15 from IC7 and IC8 its simply a matter of taking all the address and data lines across to the new memory chip, remembering that the ordering is entirely arbitrary. This will leave you with 7 unused address lines which can be switched to expand the memory up to 128 times the original amount, simple single throw switches and pull up/down resistors are compact to install. Finally ground any unused pins on the device.
Smaller + Cheaper
There are several other ways to complete this type of mod on the 606, it is possible to use the smaller and cheaper DS1230Y NVSRAM (or other devices with a single CE) by modifying the chip select logic of IC6 as shown below. Cut the traces leading to pins 8 and 5, then short together pins 8 to 9 and 5 to 6.
Now the CE signal appears only on pin 8 of IC7 and pin 8 on IC8 is a new address line. Use the multiplexer as before for the address lines of pin 15 from each chip, but now select it from the new address line on pin 8 of IC8. Run this new address line along with all the others to the new memory chip and you'll be left with 4 unused address pins for a 16 times memory expansion.
This same NVSRAM technology can be used to replace the SRAM in a TB303 or other vintage gear where you want to keep the data stored securely or expand the memory.
There are also some interesting looking NVSRAM offerings from Cypress that could be used in the same way and come in smaller packages.