Is it Legal to Incorporate in One State & Do Business in Another?

Yes, it is. 
 
When a Limited Liability Company or Corporation does business outside the state in which it was originally formed, it also needs to register to do business in the new jurisdiction(s). This is typically referred to as a "qualification" and involves filing a Certificate of Authority with each additional state in which business will be conducted.  Strong Business Credit can assist customers in qualifying to do business in any or all U.S. states. We provide this service regardless of whether the LLC was originally formed through Strong Business Credit.

Registering to do business in an additional state usually involves providing proof of registration or good standing in the company's home state. This is because most states require evidence that an LLC is formed and/or is satisfying annual requirements in its home state before granting it authority to operate in another jurisdiction.
Proof of formation is normally a certified copy of the company's Articles or Certificate of Organization, and proof of status is normally a Certificate of Good Standing. Strong Business Credit  knows the requirements for qualifying to do business in additional states and can obtain supporting documentation for your qualification.