A Sorcerer 4/Artificer one character can have two 3rd stage spell slots, but cannot Forged third level Sorcerer spells (obtained at 5th degree Sorcerer). They might, nonetheless, use their 3rd degree spell slots to “upcast” their recognised or prepared 1st and 2nd level spells for both Sorcerer or Artificer. At https://dungeons-dragons-multicla66542.liberty-blog.com/18684534/5-simple-statements-about-dungeons-dragons-multiclassing-explained