Most video switchers, even software based ones, have a baseband video output option. Examples include Newtek Tricaster that has options for both HDMI and SDI out, Blackmagic Design ATEM switchers that have SDI output, and Telestream Wirecast that can output from HDMI on your laptop or SDI via an IO device.
Other examples include Sling Studio, a wireless hardware/software switcher that works great with LiveU Solo using its HDMI output, and Switcher Studio, an app for your iPad that can output from the iPad via the lightning to HDMI output dongle available from Apple.
In all the above cases, the setup remains the same: the LiveU Solo acts as your transmission device being fed the Program Output from your switcher, via SDI or HDMI. In this way, the switcher acts like your camera - it is what plugs directly into the Solo.
You setup your Solo to the destination and settings you want, including activating Cloud Graphics if you need, and start streaming. From there, you use your switcher as you would normally, and the Solo streams the switched output to the web.