Moving from one Schengen country to another for a non-Schengen citizen

Suppose you are an American living In Spain where you have a long-stay visa. If you want to establish residency in Portugal or France can this be done without returning to the US. I would think the answer is yes since you no longer have a US address. What does this process involve? Is it possible to have more than one long-stay visa? If you want to live let’s say 4 months each in Portugal, France and Spain can you get three long term stay visas or do you have to change your visa each time you change countries? I am sure there are digital nomads who have this figured out.