> Is the same chip then available with different addresses
This is sometimes done, though more commonly in my experience is there are some input pins which the chip uses to determine the actual address.
This might be as simple as one to three inputs which should be connected to ground or supply voltage to encode the last bits of the address.
Other chips are a bit more creative, and allows you to, in addition to ground and supply, tie the address pins to the I2C clock and data pins. This allows it to generate four combinations from per address pin.