HIIT is usually a cardio type of workout. Sprints, rowing, treadmill, etc. Hit or weight training this way isn't very obvious when researching. Basically, HIIT you do for muscle benefits and fat loss benefits and cardiovascular benefits while weight training you can do separately and modify the rest intervals as needed. Short rest periods have always been available. As well as heavy weights with longer rest periods. Something to think about that may be more high intensity for weight lifting is a combination of weight lifting and body weight exercises. Like a bench press followed by a set of burpees. There are advantages and disadvantages to doing this. You could also do a circuit for time. Like a crossfit type of workout. You want to beat your previous time for the lifts. You could also just do a traditional circuit which is low rest and has many different exercises in the circuit. Also, train for intensity but less frequent workouts. Intensity in this sense means heavy. But intensity could also mean low rest periods but a shorter workout say 30 minutes. I hope this helps.