I imagine its similar to buying a firearm. You need an FFL to receive it and they background you same as they would a gun. However the FFL needs a special license for grenades as well.
Edit for those who dont know:
You can order guns online but they must be shipped to a qualified FFL. They must keep records of having done a background check and all that (same as buying in person). As an FFL you could be audited at any moment so you dont wanna screw around or the ATF might come down on you hard. Honestly the last agency I want coming to arrest me is ATF looking at their history of shooting peoples dogs. Its like they think they are above all other agencies and do whatever to arrest people.
It's much more like buying a suppressor, SBR, or machine gun since you have to submit paperwork including fingerprints anddirectly to the ATF and pay the $200 tax. This whole processes take around a year.
Grenades are registered destructive devices in the US. If you can pass the background check to buy a firearm you can buy a grenade. The cost will be $200 (tax) plus the cost of the grenade itself. Practical issues include the government being extremely slow in processing NFA transfers and finding a manufacturer that will actually sell you one. The few dealers I've found will only sell to Law Enforcement or Military buyers. There may be storage requirements I'm not aware of. E: to answer your actual question, it depends on a few factors but it may be possible to structure your grenade ownership to allow others to use it.
I assume you can put ownership of them in a trust just as many people do for suppressors, SBRs, MGs, etc. So whoever is a trustee can be legally in possession of them. All of these responsible people as they are so called, must be on the ATF form and submit fingerprints.
Yeah good luck finding someone to sell you one. Probably easier to manufacture yourself.
I don't think I've ever met someone with a permit for explosives to this day. I assume it's a right reserved for special cases, maybe military contractors that do go overseas?