Upvote:4
There is no US consulate general in the US. A consulate or consulate general is an office that represents the interests of one country in another country.
To get a new L-1 visa, as with almost all visas, you must leave the US and apply at a consulate in another country. It doesn't necessarily need to be your "home" country. Especially for renewals, it's apparently fairly common for people to travel to a nearby city in Mexico or Canada.
The only exception to the rule that visas may only be issued abroad is for diplomats and for officers and employees of international organizations such as the United Nations and the World Bank. They have their own categories of visa, and visas in those categories can be issued inside the US by special offices of the US State Department in New York or Washington. That will not help you, however.
It should also be noted that if you don't plan to leave the US, you do not need a new visa. Your stay in the US is authorized by your I-94, as noted in your passport stamp and at https://i94.cbp.dhs.gov. You only need a new visa if you need to re-enter the US after your current visa expires. Even then, there's an exception if you travel for less than 30 days to Canada or Mexico, called automatic revalidation.