1. Connect two different internet connections. Get the connections' ip addresses. In this example I'll use 18.104.22.168 and 22.214.171.124. 126.96.36.199 is the default connection, its gateway ip is used by default. You also need the connections' gateway ips, here I'll use 188.8.131.52 and 184.108.40.206.
2. In shell:
sudo echo 1 foo >> /etc/iproute2/rt_tables
sudo ip route flush table foo
sudo ip route add table foo default via 220.127.116.11
sudo ip rule add from 18.104.22.168 lookup foo
sudo ip rule add to 22.214.171.124 lookup foo
3. Now you can open different connections via the different internet connections with any program that allows you to set the binding address (source address). So for example with curl, in shell:
curl --range 0-10 http://somefile
--output somefile1 &
curl --interface 126.96.36.199 --range 11-20 http://somefile
(combine parts somefile1 and somefile2)
EDIT: fixed typo above.. "http://somefile" instead of "http://somefile2" in the second curl cmd.