If you push yourself on Body Beast with constantly increasing weights, then you will find yourself really fatigued, especially chest, leg and back days. The rep volume feels insane, especially as your weights start increasing.

The high impact T20 cardio which also hits arms, chest, and legs on a daily basis may not be the best one to combine with Body Beast.

You'll end up either putting less than 100% effort on your Beast workouts or being burned out because of over training and lack of recovery time.

This is just my personal opinion, but picking just body beast and sticking to calorie guidelines for the beast (cutting phase) should be sufficient to build muscle while leaning up slightly. Once you've finished BB and gained muscle, if you still feel heavy, you can do a round of T20 to shred, while again eating at a deficit.

You can try doing both workouts the way you suggest and see how it feels. If you are able to sustain both, then that's great.

The reason Liift4 is able to combine both weights and hiit daily is because the volume of weight training and hiit is reduced, making it more manageable. If you definitely want both daily, then Liift is also a good option as a workout. I am currently doing Liift and am pretty happy with how it's going so far.