How can I obtain items that exceed their maximum enchantment level?

I don't have an answer but perhaps a clue...

The things I've read all seem to point to using the /give command rather than /enchant. To create enchanted items using /give you need to use the Data Tag parameter like so:

/give @p diamond_sword 1 0 {ench:[{id:16,lvl:5}]}

The Data Tag is the final parameter in curly braces.

However, as far as I can tell the Data Tag parameter isn't supported in MCPE, at least not yet. When you start typing /give it doesn't list that parameter in the on-screen help. When I try entering the command shown above I get an error. I'm guessing that it isn't possible as of now but hopefully they will add support in the future.

Plug PE is a multiplayer app that allows you to do things like .g, .xp, .kill, etc.
It's $1.99 on the Apple Store and I don't know if it's available for Android.

To get a sharpness 10 diamond sword you would perform:
.g diamond_sword, sharpness:10. .g is used like this:
.g ITEM_NAME_OR_ID_WITH_UNDERSCORE,enchant1NoUnderscore:Level,enchant2:Level etc. Comma is the separator for enchantments. No spaces except between .g and the item/info

PocketMine-MP is another app with lots of proper commands (/give /enchant etc.) and it generates an OKAY new world for you. The generator needs updates but there are tons of plugins you can install for it. Mainly used for tons of player servers and not for Survival servers.

I love both apps and they both worked amazingly for me.