I remember looking into this, and remember having to make sure you match up the correct generation barrels to swap over. I decided against pursuing it, since I skip .380 (I have .32, and then I have 9x18 Mak and then 9mm Luger). For me, I stock .32 but not .380 so it wouldn't be worthwhile.
For those who ARE interested, you might take note that the Browning BDA in .380 is basically the same gun. Again like the Berettas, you have to get the correct generation to swap parts, and in this case the slide and grips wouldn't fit.
I mention that, because there are a couple sellers on gunbroker who sell "parts kits"; basically police impounds that are destroyed. They destroy the frame and sell everything else as a kit, it doesn't require an FFL to buy.
I believe the name "Gunbusters" will find them. They start at something like $38 for opening bid, and I've seen a few Browning BDA's listed over time. If you can match the correct year, you get the barrel and most parts.