Gentamicin, others. True multi-drug resistance in gonorrhea is absent in the US and Europe (so far); all gonorrhea in the US is easily treated with readily available, routinely recommended antibiotics. For gonorrhea acquired where rare MDR cases have occurred (e.g., parts of Asia including Japan, S. Korea), discuss Rx (e.g., gentamicin) with an infectious diseases specialist or your local or state health dept.
Check Sensitivities. Assuming that you know it's multidrug resistant, the lab should be able to test for different antibiotics that are out of the typical treatment regimin. Treatment may require IV antibiotics or hospitalization.
How could a multi-drug resistant (including ceftriaxone resistant) strains of n. gonorrhea be treated?
Gonnorrhoea. There are increasingly resistant strains of Gonorrhoea reported in many part of the world, including in the U.S. As such, combination therapy is advised for most cases. If resistant to Ceftriaxone, there are alternative choices, but this is best discussed with your provider or an infectious disease specialist.