A unit can't have multiple copies of the same active ability without this happening, this is due to the order id of the ability. You can see this value on the ability under the Order String field (order string/id, same thing).
For example, the Shockwave ability uses the order id "shockwave".
So when you order a unit to cast Shockwave the unit is actually issued the "shockwave" order, which tells the unit to cast it's ability with the "shockwave" order id.
If the unit has more than 1 ability with the "shockwave" order id, it chooses one of those abilities at random to cast (although I think it will pick the same ability again and again as long as it remains off cooldown).
A lot of people get fooled at this point and think, "okay, so all I have to do is change the order id of Shockwave", unfortunately, this doesn't work. Even though you can literally edit the Order Id (Order String) in the Object Editor to something else, it won't actually work. It's really just a stupid oversight on Blizzards part to even allow one to edit it in the first place since it doesn't work.
Luckily, you can use the Channel ability, a Hero ability found in the Neutral Hostile category. This ability has a special field called "Base Order Id". This allows you to assign the ability any of the Order Ids that exist in the game, meaning if you give a unit 6 abilities based on Channel, and each ability has it's own unique Base Order Id, they will all work properly.
Channel is by default meant to be a channeling ability, so you'll need to modify it to make it work like a non-channeling ability. It has a lot more control than a standard ability because it's meant to be used with triggers, so:
1) Set it's Follow Through Time to 0.00 seconds. (how long it channels for)
2) Set Disable Other Abilities to False. (whether or not it pauses the unit while channeling)
3) Set it's Options to Visible. (whether you can see the ability in the first place)
4) Set it's Targeting Options to Instant. (no targets required to cast)
Now from there you would give your unit all 6 of these new Channel abilities. You would design them to LOOK like the Destroyer Form ability, when in reality they don't actually do anything.
The plan is to trigger it so that when your unit casts one of these Channel abilities, the unit is given the REAL Destroyer Form ability that it was originally supposed to cast, and is ordered to cast it:
Events:
A unit begins casting an ability
Conditions:
Ability being cast equal to Grunt Morph (Channel)
Actions:
Add Grunt Morph (Destroyer Form) to Triggering unit
Order Triggering unit to Obsidian Statue - Destroyer Form (this is an Order with no Target)
So Grunt Morph (Channel) is your Channel ability. Grunt Morph (Destroyer Form) is the actual Destroyer Form ability that will transform your unit into a Grunt (just an example).