Here’s some guard position techniques you can do when your opponent keeps his head low, instead of postured up to pass your guard.
The grappling dummy used in this video is the Submission Master from https://grapplingdummy.net.
One reason your opponent may be keeping his head low is because he’s trying to follow you with his head to prevent you from sitting up to either side and go for a kimura lock.
In that case, you can simply push his head to one side of the other, opening him up for a variety of submissions like kimura, omoplata, guillotine, armbar and more.
You can also push his head directly away from you, throw your legs up high, and submit him with a double armbar.
If his arms are over yours, you can kick your legs up high, scissor your legs up high behind his back, s-grip your hands around your legs and squeeze for a rib crush (be careful, it’s very powerful and you don’t want to damage your training partners.)
In the next submission, you can release his arm and finish him with a fist choke.
You can also use reversals / sweeps on your opponent.
First, you can put him into butterfly guard and sweep.
If he keeps his knees too tight to you, push yourself away from him by pushing on his head or shoulders. That will give you space to hook your feet inside his legs and complete a butterfly sweep.