Yes, and the process for doing it is more straightforward than most people expect.
What you are looking for is called a special visit. Facilities have a formal mechanism for approving visitation outside of the standard scheduled days, and out of state travel is exactly the kind of circumstance that warrants one. Wardens and their staff deal with these requests regularly and understand that not everyone lives close enough to work around a Friday and Saturday only window.
The right move is to contact the warden's office directly. Do not call the general facility number and hope to get routed to the right person. Find the email address for the warden's secretary specifically, and send a written request asking what the procedures are for applying for a special visit. Putting it in writing creates a record of your request and gives the office something to respond to at their convenience rather than catching someone off guard on a phone call.
In your request, be clear about where you are traveling from, the dates you are able to visit, and why the standard schedule does not work for your situation. The more specific and reasonable your request sounds, the better the response tends to be. Facilities are not looking to deny visits from family members who are making a genuine effort to travel across the country. They just need the request to go through the right channel.
Give yourself enough lead time before the trip to get approval confirmed. Do not book travel assuming the special visit will be granted before you have something in writing.