The phrase 'another assortment of' is correct and can be used in written English.
You can use it to refer to a different group or collection of things, such as items, activities, or ideas. An example sentence might be: "I went to the store and picked up another assortment of ingredients for dinner."
The changes made in the catalog's organization include a quick-reference gift index, showing presents for under $25 and another assortment of presents for under $50.
Shikar is a game bird (guinea hen, the night we ordered it) in a brown sauce that features another assortment of Kashmiri spices and the intriguing lotus root, an appealingly chewy tuber that looks in cross-section like an old-fashioned rotary phone dial.
If not, another assortment of rays needs to be launched.
Long after most people had lost interest in - and the media had stopped writing about - H5N1 bird flu, we now have to get used to another assortment of letters and numbers.
At a short distance, in another assortment of coverings, were traders busy selling kebabs and luxuries radios, bolts of cloth, pointy-toed leather shoes.
Sounds like another random assortment of local radio presenters; they're reading quotes from Heat magazine, with hilarious consequences.
Her bathroom was a frilly gift that one girl might give to another, an assortment of powders, soaps, oils, lotions, perfumes, sea sponges, lava stones, and so on.
Finally, I stopped at a couple of florists to fill one vase with daffodils and another with an assortment of parrot tulips and sweet pea.
The pace is leisurely: one spread is devoted to a collection of beachcomber's finds — mussel shells, seaweed clusters, hinged claws — another to an assortment of clouds.
I had a bit more bulgur, couscous and brown rice on hand so I used them for more substantial salads, one that combined bulgur and greens, another that mixed an assortment of different grades of brown rice and a little bit of farro with roasted red peppers, herbs and feta.
Another displays a horrifying assortment of weapons.
