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I want to make 3 squads of Vanguard Vets, all with Power Mauls and Axes.

Issue is, it doesn't come with NEARLY ENOUGH bits.

Where do I get more?

The D-Watch Vets come with 2 mauls and the SM Assault Squad comes with one axe. I'm sure E-bay can help here.

There are also the third party companies like Kromlech and Anvil.

Power mauls from deathwatch vets.
You get plenty of them and barely anyone uses them lol.

There should be a ton on eBay for cheap.

not sure they're exactly what you need but the AoS Orruk Ironjawz have axes/mauls that look exceedingly close to chainsword types imo

Ebay is definitely the place to go, I have seen mauls from sellers like bitz world and window-box. Only question is what style you're going to go with, how you're going to keep it consistent across the units, and how much you want to pay for each bit. For example, the "baseball bat" power mauls from SM kits look like they're around $2.50 each, whereas you might pay that much for 3 of something else that you can convert onto your models with a bit of work.