iConnect Midi and Audio +4 will change the one ASIO device limit soon, (maybe)

I wish I'd had something like that when I was making the transition from my old computer to the new one and still working on both. My Focusrite interface has two Firewire ports, which might suggest you could hook it up to two computers, but sadly that is not the case. It's just for daisy-chaining two interfaces.
 
Too bad this new interface has only 4 audio channels. But at $300 I guess you could get two. Here's the product page.

Since the thread referenced is mine, I guess I'd better chime in.
A year later, the iConnectMidi4+ is an awesome device, for MIDI, only. I have the audio pass-thru feature disabled.
iConnectivity did not release an audio driver for the device. Instead, they recommend use of ASIO4ALL. While that driver works fine when only using the ICM4+, it's promise of aggregating various audio devices is still just that (for me). ASIO4ALL doesn't work well when aggregating my Focusrite 18i20 and the ICM4+. The Focusrite really needs to be using it's own ASIO driver, and it can't do that under ASIO4ALL.
The ICM4+ excels at MIDI. I have a 2013 MacBook Pro, my main Windows 7 Pro studio desktop, iPad 1, iPad Air, two DSI Mopho's, Nord Lead 2x, Waldorf Q, CZ-5000, Electribe-A, and (3) controller keyboards all configured through the ICM4+, and all can pass midi back-and-forth without special accommodation. I regularly use my nord as a controller for Arturia's iPad apps. My Macbook and iPads are configured to talk to the ICM4+ across my wireless network and experiences zero latency (for practical purposes).
The Configuration software that iConnectivity provides has a dreadful UI and is painfully incomprehensible. However, once you figure it out (hours of effort and a lot of trial and error), you can find tune your device communication channels in myriad ways.  The software also will either not open or regularly crashes when I have any software that uses one of the configured devices running.  The version of the configuration utility that is available for the iPad is far easier to use (though still awful to look at) and never crashes.
 
Now, the new beast: the iConnectAudio, has it's own drivers, so you need not go the ASIO4ALL route. While the device can be tapped simultaneously by drivers running on both your Mac and Windows machines, it cannot run alongside other audio interfaces on your windows machine. You would still need ASIO4ALL for multiple interface aggregation on Windows machines. OSX, of course, doesn't suffer this problem. I'm holding out hope that Windows 10 will include driver aggregation.
 
Back to the OPs query: The iConnectAudio does not allow for multiple interfaces to be connected to one computer, but it does allow for one interface (itself) to be connected to multiple computers.
 
Finally, to the OP, I cannot recommend the 18i20 highly enough. Your rationale for considering it matches mine precisely. I've had it about 18 months now. The mic pres sound every bit as good as the ones on my dedicated and far more expensive Focusrite preamp. Everything you need to control it is right on the front panel, including a power switch. Why do so many companies put the power switch on the back, if it has one at all? I digress. It never needs troubleshooting of any kind. I can easily swap the USB cable between my mac and windows machines and everything registers correctly within seconds. I'd say it's second only to my Nord Lead on the awesome scale.

Michael,
If I were regularly recording drums I'd already have the OctoPre. I don't do a whole lot of live micing, though, so the two front panel inuts on the 18i20 are just fine for now. My setup is mostly hardware synths and effects. I gave up on the notion of having them all wired to daw inputs simultaneously. Instead, I run everything to patch bays, lots of patch bays.

I am another user of the ICM4+ and also use it midi only.. From a midi perspective it is like a grown up Motu micro xpress in that it is a standalone midi router for non PC use so has many applications, not least of which is slaving a iPad into a desktop system.
One particular feature that is very impressive is the midi filtering, which is very useful when dealing with synths that have different CC maps.