Beams stands for Breakthrough Engine with Advanced Mechanism System, or for us mere mortals....Bought Engine Another Mortgage.
And yes, the lightweight reciprocating internals, 11.1 comp. ratio and VVTLi do not lend themselves to turbocharging.
If you want this motor so you can mount it inline in a RWD car, its good, but needs high revs to work and is $$$. Better off cost wise to go a 3S-GTE from an MR2 Turbo. And if you really want to impress this list and spend $$$, buy a 3S GE Beams block and add the GTE head and turbo. Now that would be a project.
Mitch.