Yes. Your domicile state - the state in which your main home/permanent residence is located - can tax all your income, regardless of where you earned it.
Other states can tax you as a non-resident on earnings from work actually performed within their borders, if the income exceeds their filing threshold for non-residents. Location of the employer's home office doesn't matter; taxation is based on where you actually work (and live).
You can take a credit on your home state return for taxes paid to another state, so you won't be double-taxed.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.