No there's only one elite four.
The one you battled before Kanto, The Elite Four of SoulSilver and HeartGold are shared between Kanto and Johto even though it is located in Kanto. But once you beat Red the Elite Fours teams are updated so technically those are the elite four.
Defeat the Elite four and catch the boat from Olivine to Vermillion
Beat the elite four. Professor Elm, I think, someone, will give you the boat pass for the harbor in Olivine, which will take you to Kanto
You must beat the Elite Four. Then take the ship in Olivine City which will take you to Vermillion City
Once you've beten the jhoto and kanto gyms and elite four you will have the option to face red {the character in blue and red} When you beet him prof oak will reward you with 1 kanto starter.
YOu will find the alite four slightly off a island.
You go to the Cerulean Cave after beating all eight Kanto gym leaders.
u get to go to the Kanto region after you defat the eliet four
Once you beat the elite four and the champion professor elm will give you a s.s. ticket to get to the kanto region
In HeartGold and SoulSilver, yes, you will be able to go to Kanto and travel mostly its entire region which includes battling the Kanto Gym Leaders, but first the Elite Four. After, you've gotten all 8 Johto badges, talk to Prof. Elm and he'll give you a ticket to S.S. Aqua, which will take you to Kanto.
he will give you the national pokedex then when you go to kanto he's in pallet town in his lab
to fight the elite four after obtaining all of the kanto badges, just head back to where you faced them earlier after getting all the johto badges