The key with the OO vowel in my experience is to think of it as an AH with the lips closed. A great exercise for this is the OO>OH>AH scale where you start on an OO and gradually open it to an AH. The only thing that you should feel change is the lips. If you feel it changing in the back with the lips then you wnat to work on separating the two.

Doing scales on AEIOU while feeling like they are all one vowel is also a very excellent exercise.
When all vowels are strong and their modifications done properly, you won't feel like you are going from a strong vowel to a weak vowel, they will all feel similar to a single vowel in the throat. This is because as we get good at singing we want to minimize excessive vocal tract shifting (only getting the necessary amount of change in the throat to make the sound we need to make).

At first you may need to go lighter on EE and OO because you are weaker at them, as you get a handle on keeping the throat open you can lean more into them. This is where the vowel modifications help because taking EE to an EH in a way that's too blatant can act as a crutch until you learn how to make it subtle. (same with OO).

Next time we have a lesson we can spend more time on EE and OO.

EE, OO and AH all have their particular "challenges", but specially the EE needs some care to be adjusted well. Being able to relax tongue and jaw, keep a good quality of emission and adjusting it well on chest voice first is very important before you try to consolidate it higher.

I personally found EE harder, but that was simply because I had bad closure issues. My EE didn't have the proper focus like it should have. Overall, though, I can't necessarily say one is more difficult than the other; each is just unique in how it functions. I actually have to use my EE to make my OO clearer sometimes, and other times I have to use my OO to position my EE properly! So it works like this. If I'm in my middle range going into the first bridge (so say from C4-G4) on an EE vowel, I'm thinking some of the shape of an OO in the back of my throat. (More properly, it's a French U rather than just an OO.) I do this to prevent the larynx from feeling jammed up. It also allows you to get more chest active. If I'm singing OO in that same range and I find it wants to get overly dark, then I shade it more towards EE by saying EWWWW like when girls see something disgusting. That bring out more of the ping and upper overtones in the sound.

Now, when you start going higher, that's when things get interesting. For both vowels, the mouth has to gradually open more as though you're going to say AH (at least if you're trying to keep the upper overtones). A pure OO in terms of how you would normally speak it, does not exist as you get closer towards a high C (at least not in full voice). It begins to mix with other vowels in order to keep the resonance high. If you try to approach it the way you would speak a normal OO, it will get throaty and muffled. To me, it feels more like I'm saying U as in "book", but with the mouth open as though I'm saying AH. It also gets shades of UN as in "onion" or "fun", which gives it that high end ping. It's a really odd feeling and it's just something you have to get used to.

As for EE in the upper range towards high C, the mouth opens more like AH, but it's almost as though you're pronouncing IH (as in "bit"). If you start to lose your chest connection as you do this, the larynx will come up and the sound will get excessively thin. You really have to stay anchored in your support and chest connection. The sound will get very bright, though. Allow you will hear is the brilliance in the sound rather than the more bassy middle resonance like you would hear in your middle range. If you try to make these high notes have that same bassy resonance, you will constrict yourself. As long as you keep your chest connection, the bass element will be there.

Darryl Pass here is a perfect example of how to approach both of these vowels. He keeps the placement (the high end ping) consistent between both of them. Check out "endure" at 1:07, "do" at 1:16, "seems" at 1:22, "through" at 1:38, "through" at 1:44, "give" at 1:56, and "give" at 1:59.

In this clip of David Phelps singing "These Are They", you can hear (and see) the same thing. "Door" at 3:27, "these" at 3:30, "tribulation" at 3:38, "in" at 3:45, "into" at 3:59, "jubilation" at 4:02, and "redeemed" at 4:16.

In this clip of Jared Shanklin singing an impromptu performance of "Soon As I Get Home" with Faith Evans, you can hear him doing tons of OO vowels (although it's a little hard to hear over the crowd). He sings from 5:00-6:00. Especially pay attention to the "soon" at 5:37. When he jumps up to the second note, you can see him open the mouth more and let the vowel open up a bit (towards U as in "book") so it doesn't get overly closed. That's what you have to do going towards high C range. Listen to how much ping the voice keeps.

Here is a clearer video of Jared doing a reprise of "Kissing You". Listen to the "you" he does at 0:42-0:44 when he goes back and forth between the G4 and A4. Hear how much ping and focus the voice keeps while still maintaining an intelligible OO quality?

In this clip of Zack Dobbins singing "Anthem", listen to the "would" on the A4 at 1:57. The approach was perfect! That's what the vowel should sound like in that range. It picked up more of the upper resonance -- the sinus resonance.