Well, it's your game, but I wouldn't allow it.
It's very clearly NOT part of the standard rules, so its a GM call.
Stuff like this really needs a facility and an entire design crew to create, though. It's not like firearms where a guy could in real life machine one in a shop.
The ONLY place in Shadowrun you'd see this is in military hands, as a military project. Because, let's face it, it's a military grade weapon.
And of course, being a military grade weapon, once the powers that be realize what it is that's tearing up the streets in the hands of a shadowrunner, they're going to answer it with military-grade responses.
The runner won't even see what killed him and took out half a city block. If he's lucky he might hear the whine of the incoming airstrike.
This is Shadowrun, not BattleZone 2070s. Most of the time, anything more than pistols/SMGs will get the SWAT team called in. Anything more than assault rifles or maybe LMGs will get military scale assets in response.
Shadowrunners can and do use heavy weapons, it's true. But every time, it's for extreme situations, and once you start firing them, every good 'Runner know that a countdown clock has started. If you're not long gone before it hits zero, you're dead. Just dead, no matter how bad-ass you think you are.
-k