A process for producing steel and for obtaining slag having a high content of additional elements such as vanadium in a two-step process. Liquid pig iron is initially blown onto a high-grade slag at a lower temperature, the slag being further processed separately after tapping, while the pig iron is supplied to at least one additional converter in which it is blown at a higher temperature to form steel. A high-grade slag is generated while shortening the steel production process using the process in that the intermediate metal product that is tapped from the first converter is subjected to a heating and/or holding phase before being supplied to the second converter.