Yes you can use SPI to connect as many things together as you want. There are three pins that are used for data and clock. A Master device must decide which device it is talking to by asserting a chip select signal. This mechanism accomplishes the same function as the addressing mechanism used in I2C. Clearly with one clock and one data line the transactions are one way at any given time.
In SPI, the data transfer is an exchange. When the master sends 8 bits out the slave device sends 8 bit back at the same time. That is why there are two data lines.
I've used SPI for Display Controllers, I/O Expanders, DACs and A/D converters. Never had a single problem with it.
What you cannot do is have both PICs trying to assert the eeprom chip select at the same time. That way lies chaos!