One of the more well-known comorbidities commonly found in Psoriasis patients is Type II Diabetes, often as part of metabolic syndrome. There are several interesting therapies for each of the diseases that have the possibility of improving the other, including metformin and GLP-1 inhibitors.
Metformin has a 70 year history of first-line use in the treatment of type 2 diabetes and has a number of mechanisms of action that reduce the amount of hepatic gluconeogenesis. It is generally a well-tolerated and inexpensive drug, which has led to a variety of clinical research in non-diabetic conditions such as non-alcoholic fatty liver disease.
As of today, there have been a few trials of metformin in dermatological conditions, most prominently acanthosis nigricans, which is an obvious candidate due to its linkage to insulin resistance and blood glucose levels. One pilot study showed a significant 28% increase in psoriasis patients reaching PASI 75 on metformin monotherapy.
Whether this positive anti-psoriatic effect is direct or mediated through positive improvements in metabolic condition (the same cohort saw improved BMI, blood pressure, etc.), is debatable.
Certainly, decreases in BMI strongly correlate to improvement in psoriasis, to the point where bariatric surgery may be beneficial in morbidly obese psoriasis patients. Metformin therapy typically induces moderate weight loss in obese patients, but it may well have a direct mechanism(s) as well.
Although metformin’s primary mechanism of action is thought to be activated protein kinase, it also has some effect on Glucagon-like peptide-1 (GLP-1). GLP-1 specific antidiabetic drugs also seem to show anti-psoriatic effects. For example, there are a number of case reports showing skin improvement in psoriatic patients taking Liraglutide, a GLP-1 agonist, before any improvement in glycemic control or weight loss occurred.
It seems that for diabetic psoriasis patients, a treatment regime that includes oral antidiabetic agents known to also improve psoriasis is worth considering, and is unlikely to cause drug interactions with other psoriasis therapies.
 Giri, Alsaffar, and Ramakrishnan .Acanthosis Nigricans and Its Response to Metformin.Pediatr Dermatol. 2017 Sep;34(5):e281-e282. doi: 10.1111/pde.13206. Epub 2017 Jul 30.
 Singh and Bhansali. Randomized Placebo Control Study of Metformin in Psoriasis Patients with Metabolic Syndrome (Systemic Treatment Cohort).Indian J Endocrinol Metab. 2017 Jul-Aug;21(4):581-587. doi: 10.4103/ijem.IJEM_46_17.
 Debbaneh,, et al. Diet and Psoriasis: Part I. Impact of Weight Loss Interventions. J Am Acad Dermatol. 2014 Jul; 71(1): 133–140.Published online 2014 Apr 4. doi: 10.1016/j.jaad.2014.02.012
 Sako, Famenini, and Wu. Bariatric surgery and psoriasis.. J Am Acad Dermatol. 2014 Apr;70(4):774-9. doi: 10.1016/j.jaad.2013.11.010. Epub 2014 Jan 7.
 Al-Badri and Azar. Effect of glucagon-like peptide-1 receptor agonists in patients with psoriasis. Ther Adv Endocrinol Metab. 2014 Apr; 5(2): 34–38.doi: 10.1177/2042018814543483