Yes multi website supported by Marketplace Basic Extension.
Suppose a vendor signs up with the website 1 and he wants to sell the products on website 2 also in the same magento. There are two ways he can sell his products first is he can sell by creating a new vendor there and start selling his products.
Else there is also an option from admin from which admin can make vendor allowed to sell his products in both website he can go to the System Configuration -> Customer -> Account sharing option -> share customer accounts make this to (global)
Then the same vendor will be applicable for both the websites.
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