It depends. There's no one-size-fits-all answer. Some things to consider though:
- how far do you have to travel
- will you be traveling by plane or car
- what is the weather like in that part of the country at that time of year
- will you be taking that month off, or will you be on a rotation that you have to get back to
- what are your financial constraints like
FWIW, I found interviewing to be exhausting. If all of your interviews are local, one-day affairs, I wouldn't schedule more than 3 per week, personally. I needed a day between interviews to relax and refresh myself a bit.
If you'll be traveling far, especially if you have to take weather into account, you'll still want at least one day off between interviews to allow plenty of time for travel (and the inevitable delays).
Last tip, which has been posted here many times: if traveling by plane, DO NOT check your luggage! Don't let your bag with your interview suit out of your sight. 🙂