No, the ATmega328 is limited without a chance of expansion, the Arduino Mega 2560 could help with more SRAM on chip and the possibility to add external SRAM.
But there are still some possibilities for the ATmega328 left. You have EEPROM and Flash to store (static) data. What do you store in the array? Boolean values? If that's the case you are wasting space. You could pack 8 bits into a byte by changing your data format. Arduino is too slow? Maybe your code should be optimized: digitalWrite() is slow but writing the registers directly is not that complicated.