Technically speaking there is no maximum amount of suboxone per day that a patient should be administered. Because of the variability in patients' responses to treatment and the huge differences in the length and dependency of their addiction, doctors are only given guidelines on how to prescribe suboxone.
Generally speaking the best method is to begin by taking suboxone under observation so that your doctor can figure out the correct dosage for you over the course of 2 or 3 days. They will likely administer suboxone in small doses (2-4mg) multiple times over the course of the day to fight off your initial withdrawal symptoms. The first day it is usually recommended that no more than 8 mg is taken, and no more than 16mg on the second day of your treatment. After this period of your doctor will be able to better understand what your dosing requirements are and you should be able to go onto a once-a-day treatment plan where you receive a regulated dose of suboxone.
Most patients stabilize on a dose of around 12-16mg which will be tapered down over the long term. It is possible that your doctor will prescribe you a higher dose of suboxone than this but ordinarily doses of over 32 mg are thought to be inadvisable as the effects of the drug begin to plateau. Although there are those that argue that these doses are quite high, it is good to remember that suboxone is a lot harder to overdose on than other opioids. It's best to take what seems like a high dose at first because it will be effective in fighting your withdrawal symptoms. A sufficient dose will also curb the temptation you would otherwise have to satisfy your cravings with other opioids or benzodiazepines, both of which would significantly increase your chances of an overdose.