If you just plug in the additional 412L you will be under the minimum recommended impedance (into the "meltdown" rage for the Beta), AND
twice the power going to the 412L would be going to the 10's.
To each their own, but as Isaac says; "I wouldn't".
If you can cobble together a wiring scheme that
will work depends on what the impedance of the actual drivers in the cabinets are.
Most 4 driver cabinets are wired series/parallel, and if that's the case the Beta has 4 ohm drivers and the 412L has 8 ohm drivers. If you are correct that the 4 10's are paralleled, they are 16 ohm drivers.
Regardless, you would probably have to replace the drivers in one of the cabs to make it work properly. Two 8 ohm cabs would be what you are shooting for.
In a 4 driver configuration you have three choices;
The same impedance as the individual drivers, series/parallel.
or
25% of the impedance of the individual drivers, parallel.
or
4 times the impedance of the individual drivers, series.
By process of elimination the only practical solution is to get 8 ohm drivers for the Beta. UNLESS... the Beta in question
already has 8 ohm drivers; which I mention because you haven't actually seen the one you are considering, and more importantly because
my Beta lead 410 combo had 8 ohm drivers in it from the factory, so it's a possibility.
http://sunnforum.ampage.org/index.php/topic,5252.msg20859.html#msg20859