The MIDX-20 from Primova Sound that
@DLC86 mentioned is a great little box; I have a couple and they're very handy. They are programmable so you can customize your MIDI routing between the ports, and keeps you from having to include a full-blown computer into your rig. Depending on how you set things up, you may not need one though.
@pauliusmm -- you mentioned wanting to use a mi.1 Bluetooth interface with the Axe-FX III. Since that's Bluetooth LE to MIDI ports, you shouldn't need USB at all; you just need more MIDI ports, which you can get with MIDI splitters/mergers.
MIDI Solutions is the place to check out for those. If you need to double up on both ports, two of their Mergers will do the trick -- they work as both a merger (2 into 1) and as a splitter (1 into 2) for both your MIDI input and output. If you need even more MIDI, they also have the Quadra Merge and Quadra Thru with 4 ports to play with.
Another Bluetooth LE option if you're not married to the mi.1, or you want to add USB for some other reason, is the
puc+ from Zivix. It can do MIDI via a MIDI cable or USB, and supports bidirectional MIDI when using USB. I use one of these in my rig for doing page turns on my iPad (in forScore) from my foot controller; works great. If you want to use it via USB though, you will need a box like the MIDX-20 to connect everything up. (puc+ to MIDX-20 USB port; Axe-FX III to MIDI in/out; additional USB port available for more MIDI connectivity)
Having said all that, if you're looking to get more advanced with MIDI and want a nice foot controller to drive it all, I'd recommend checking out the Mastermind options from
RJM Music. The Mastermind GT is an absolute beast; it's the brains of my rig, and I've used it to run entire shows from my feet (several vocal processors and Axe-FX units) while playing guitar at the same time. Even the Mastermind LT, their least expensive model, has the same levels of programmability for controlling a multitude of devices -- and all have native support for the Axe-FX III. Not necessary if you're just using the iPad to select patches, etc, but very nice if you're looking to do more (and with your feet).