Apart from kneeling and lying one leg at a time quadriceps stretching poses, other options for stretching the quadriceps include stretching them while standing, while in various lunge type postures like pigeon, low lunge and splits, using a wall and lying on your belly.
For a double leg lying quadriceps stretch check out virasana yoga pose.
If you can't touch your butt to your heels while kneeling or squatting, then squatting is another possible position for not only stretching your quadriceps muscles but also strengthening them.
For knee stability, try squatting with the heels lifted.
One of the nice things about stretching the quadriceps while either kneeling or lying is easy to activate the quadriceps (or relatively easy) by just pressing the foot into the floor.
You may find that activating and relaxing your quadriceps slowly, repeatedly, and rhythmically, makes it easier to stretch them. You may find that you can go deeper into the stretch on either the active phase or the relaxed phase.
With the standing quadriceps stretch it may be a little bit more difficult to activate your quadriceps. You'll have to work at pushing your foot or your ankle (whichever you are grabbing) out of your hand or hands. So you'll have to have a good grip.
So a bonus here is you'll not only strengthen and stretch your quadriceps, you'll also strengthen your hands.
The usual way to stretch the quadriceps while standing is to stand upright. You can start with the knee forwards so that the focus is on your quadriceps, then move your knee back so that you also stretch the hip flexors. Another option, while standing, is to bend forwards.
It helps if you can touch the floor with your hand. If not, use a chair or yoga block for your supporting hand.
Initially start with the knee close to your chest, then move the knee back and up to deepen the quadriceps stretch.
You can do a similar stretch in a low lunge. With some padding under your knee, (you might like to fold you mat over for comfort) first move your hips back and grab your foot. Then move your hips forwards and down. Sink your hips.
You might have to start with your arm straight. In this pose the hip flexors are also stretched and they may inhibit the degree to which you can stretch your quadriceps. Try resisting the stretch by pushing your foot back against your hand.
As both sets of muscles loosen up, then bend your arm and increase the knee bend to deepen the quadriceps stretch.
If you like you can try shifting your hand position so that you are pushing on the foot instead of pulling it. To get this hand position you may find it helps to move your hips back first, get your hand in position then sink your hips, then push your foot forwards.
Note that this requires some shoulder flexibility and if you can't already touch your butt to your heels while kneeling, or better yet, get your butt to the floor in hero pose, then you may not be able to do this option.
An interesting variation of this stretch is to grab the foot with the opposite hand. Start with your hand on the floor, pull your foot forwards and sink your hips. Then, try to place your elbow on the floor.
Using pigeon as a quadriceps stretching pose, you'll probably have to support yourself with your front leg hand. Grab the back foot and pull it forwards. If possible, adjust your hand position so that you can push your foot forwards.
Here, scapular control may be important. You may have to relax your scapular muscle enough to get your hand into position. Then, stabilize against retraction so that you can use your hand to push your foot forwards.
For the quadriceps stretch, first resist the stretch by activating the quadriceps. Use it to push your foot back against your hand. Then after a brief pause, relax your quadriceps and push your foot further forwards. Repeat a few times, or until this method ceases to be effective. Then just hold the quadriceps stretch.
You could also front to back splits as a quadriceps stretching option.
Laying prone, with your belly downwards, you can stretch one quadriceps at a time or both. Starting with one foot, bend the knee and pull the foot forwards.
To get the hand in the "push" position, prop your torso up using your free hand. Also, it may help to use your spinal erectors to bend your spine backwards and lift your chest.
As you try to get the hand into the push position, activate your quadriceps so that your hand has something to work against. That in combination with using your spinal erectors may make it easier to get your hand in position. Then, once the hand is in position, you can relax the quadriceps.
Then activate your quadriceps to resist the hand, then relax it to see if you can push the foot further down and stretch the quadriceps further. As you go deeper, move the foot to the side so that you push the foot towards the floor to the outside of the thigh.
When pushing down, pay attention to your knee. Work at smoothly pushing down as opposed to suddenly pushing down so that you can stop if you need to.
The double leg stretch, called frog pose, is a technical challenge. With one foot in position you may have to activate the quadriceps to give that hand and your torso a stable foundation. With the spinal erectors also active you may then be able to get the other hand into position.
Why improve muscle control?
Muscle control not only helps you to control your body, it also helps you to feel it.
Muscle activation creates the tension that not only moves your body, but helps you to "sense" it.
With better muscle control you can use your body with less effort and make it easier to balance, improve flexibility and deal with pain and poor posture.