Yes. Every state allows business entities from another state to own business entities in their state. Whether its worthwhile doing it depends on the details of your business.
If you are the sole owner of LLC A and LLC A is the sole owner of LLC B then for federal income tax the LLCs are disregarded. If Both LLCs are in the same business then you are simply the sole proprietor of the business for federal income tax and would do a single Schedule C to report the income from them and attach that to your Form 1040. If they conduct two separate businesses then you'll be considered the sole proprietor of both businesses, and you'd do two Schedules C.
How state taxes will work will depend on the states in which the businesses are organized and, if different, the states in which they operate and are managed.