The standard Octopre or similar things by Audient or even Behringer are a great way to add more inputs. And have only ADAT outs, meaning they can't accept digital audio inputs from your master interface, they are just used to add more A/D inputs to your system.
However some models of the Octopre also accept ADAT inputs which can be routed to the units analog line outputs on the rear panel via the 'ADAT > line' button. These can be used simultaneously to the units ADAT outputs > recording interface. Such versions of the octopre (eg. the Claret+ Octopre) can add 8 additional inputs and 8 additional outputs to an interface equipped with ADAT ins and outs.
Apart from the higher end Octopre's with this feature the only other device I know of (though there may well be more) is the RME ADI-8 MkIII which is also a 2 way expansion to the RME fireface, but should work with any other ADAT equipped device.
One ADAT cable will carry 8 channels of audio at lower sample rates (44.1Khz, 48Khz), each cable only carries 4 channels of audio at higher sample rates, hence they tend to get provided in pairs, and you will need to use both for 8 channels at higher sample rates in either direction.
Each ADI-8 or suitably equipped Octopre would add 8 inputs and 8 outputs via two ADAT cables (one in, one out) ADAT at lower sample rates, and 8 inputs and outputs via dual ADAT cables (two in, two out) at higher sample rates. Unfortunately you can't use both ADAT's at lower sample rates to get 16 channels of audio in a given direction because at that point you are limited by the physical number of analog connectors these two particular devices have.
You also have the option of getting an extra couple of outputs from the SPDIF I/O's, on top of the analog I/O's and ADAT. If an interface has both SPDIF and AES/EBU then often they are tied, so the same signal goes to both.
As pointed out by one of the other answers, things have moved on, in terms of features of the gear available compared to my experience when I first wrote this answer. I wouldn't be surprised if there are more standalone ADAT D/A A/D converters around now other than the RME unit and the higher end Octopre's, it's not before time too!