When you receive a J1-Working Visa and currently work in America - Can you apply for a second J1-Visa in a different company/university to start directly after finishing your program of the first J1-Visa? I couldn't find any restrictions, but sometimes people say you have to wait for at least 2 years in your home country to be allowed to apply again.
There are 12-month and 24-month bars if your new program is in the "Research Scholar" or "Professor" categories only (not other J-1 categories):
If you were previously finished a program on J-1 as a "Research Scholar" or "Professor", then you cannot start a new J-1 as a "Research Scholar" or "Professor" again within 24 months.
If you were in any J-1 or J-2 status for more than 6 months, you cannot start a new J-1 as a "Research Scholar" or "Professor" within 12 months after that.
Note: Don't confuse this with the INA 212(e) 2-year home residency requirement that some J1's have. That is a restriction upon getting an H or L work visa or permanent residency, which is irrelevant because you are not getting one of those.