I've spent a lot of years locating Arkansans serving in the regiments of other states, Union and Confederate, and have added them to my database as I run across them. In some cases, there were entire companies of Arkansas troops attached to "foreign" regiments -- notably Kentucky, Louisiana, Missouri, Tennessee, Texas, and the Indian Territory. Wirt Adams' 1st Mississippi Cavalry included a company that, if not an official Arkansas company (can't tell for sure), was predominately composed of Arkansans. The 3rd Confederate Infantry was predominately an Arkansas regiment, and there were individual Arkansas companies in a couple of other Confederate regular regiments.
In addition, I've found individual Arkansas soldiers serving here and there in the regiments of other states, usually because of a family connection. For example, I found a Columbia County man who returned to his birthplace in South Carolina to enlist, as most of his brothers had remained there and enlisted.