Methylene blue may be considered a rescue therapy in catecholamine-resistant vasoplegic shock patients, but there is insufficient evidence to support its use as a first-line agent. It can be used for norepinephrine-refractory vasoplegia developed due to cardiopulmonary bypass, systemic inflammatory response syndrome (SIRS), burns, or anaphylaxis without the development of side effects. A dose of 2 mg/kg given intravenously (IV) as a bolus followed by continuous infusion is recommended, as plasma concentrations are greatly reduced in the first 40 minutes. The lethal dose is 40 mg/kg. A single dose of 1.5 mg/kg may also be effective at reducing morbidity and mortality from vasoplegic shock. It is reported that methylene blue may lead to severe serotonin syndrome when combined with other serotonergic medications. 
In a 2016 systematic review on twenty years of vasoplegic syndrome treatment in heart surgery, the authors mention that the most used dosage of methylene blue is 2 mg/kg as an intravenous bolus followed by the same continuous infusion because the plasma concentrations are greatly decreased in the first 40 minutes. Methylene blue is safe and effective in the treatment of heart surgery vasoplegia in recommended doses, but the dose of 40 mg/kg can be lethal. Some authors use a loading bolus of 2 mg/kg in the cardiopulmonary bypass (CPB) and follow with a continuous infusion of 0.25 - 2 mg/kg to ameliorate refractory hypotension for patients undergoing valve replacement surgery. Doses of methylene blue up to 7mg/kg have been used in some reports with no side effects. The authors propose a total dosage of up to 10mg/kg may be used in extreme cases. [2-3]
A 2013 article recommends a dose of 1 to 2 mg/kg as a single bolus based on the existing literature and safety profile. The authors mention that although the dosing regimen for methylene blue used in clinical data is not completely clear, it seems to be consistent in a range of 1 to 2 mg/kg, which is similar with the treatment of methemoglobinemia. However, the article cited studies showing that a dose greater than 7mg/kg was associated with adverse effects such as paradoxical induction of methemoglobinemia, acute hemolytic anemia, and detrimental effects on pulmonary function. 
Another article recommends methylene blue used as a single dose of 1.5 -2 mg/kg IV over 20 min to 1hr for rescue treatment of refractory vasoplegia. This article also supports that methylene blue is safe when used in therapeutic doses (less than 2mg/kg), but it can cause toxicity in high doses due to its monoamine oxidase (MAO) inhibiting property. The authors mention that the dose greater than 5 mg/kg can precipitate fatal serotonin toxicity and rarely cause severe anaphylactic shock. 
Per Trissel's IV compatibility, methylene blue is only compatible with dextrose 5% in water (D5W). It has not been tested in Dextrose 10% in water (D10W). Methylene blue is also incompatible with dextrose 5% in sodium chloride 0.9% (D5NS), dextrose 5% in sodium chloride 0.45% (D5W 1/2 NS), normal saline (sodium chloride 0.9%[NS]), and sodium chloride 0.45% (1/2 NS). Methylene blue has not been tested in dextrose 5% in lactated Ringer's (D5LR), Lactated Ringer's Injection, or Ringer's injection. No results can be found on its compatibility with Plasmalyte solution, however, it can be reasoned that lactated Ringers and Plasmalyte will not be compatible due to their chloride content.