Can I carry contact solution onto a plane that is more than the 3oz limit?

The TSA is unclear on this. Quoting the TSA:

3-1-1 Liquids Rule Exemption

You may bring medically necessary liquids, medications and creams in
excess of 3.4 ounces or 100 milliliters in your carry-on bag. Remove
them from your carry-on bag to be screened separately from the rest of
your belongings. You are not required to place your liquid medication
in a plastic zip-top bag.

However the TSA elsewhere states:

Medically required liquids, such as baby formula and food, breast milk
and medications are allowed in excess of 3.4 ounces in reasonable
quantities for the flight.

and elsewhere:

TSA allows larger amounts of medically necessary liquids, gels, and
aerosols in reasonable quantities for your trip, but you must declare
them to security officers at the checkpoint for inspection.

(this last one is the the quoted above by phoog, and is the exact rule quoted when you search their website for ‘contact lens solution’)

My understanding is that the first quote is the official rule, and it is the rule most prominently posted on the TSA’s website, however I would not rely on it.

Note that I have also had a similar experience with contact lens solution where one officer actually explicitly told me it was allowed, and another explicitly told me it was not.

What was interesting is that in my case, with the rules as written at the time, it all revolved around the liquid bag itself: There was an explicit rule that said you cannot have contact lens solution in quantities over 100ml in your liquid bag and there is a different rule that says you are allowed medically necessary liquids in unlimited quantity. The combination of the two is that if you have large quantities of medically necessary liquids, you are not allowed to have them in your liquid bag, but you can carry them on

…and I actually had a TSA officer make me remove my contact lens solution from the liquid bag so that it met those rules. Apparently my contact lens solution becomes less safe when it’s in the liquid bag.

You quote the TSA:

Medically required liquids, such as baby formula and food, breast milk and medications are allowed in excess of 3.4 ounces in reasonable quantities for the flight.

The key is “reasonable quantities for the flight.” For most people, 3.4 ounces of contact lens solution is far more than would be needed for a single flight. If you need more contact lens solution than that for use at your destination, you are supposed to put it in your checked baggage. For longer trips, therefore, you would need two bottles: a small travel bottle for use on the plane and a larger bottle for use after you arrive at your destination.

I don’t know why the TSA would have allowed you to take a larger bottle on the domestic flight. I can imagine that any of several reasons might apply. For example:

• The TSA officer may have been unfamiliar with contact lenses, and therefore unfamiliar with the amount of solution one typically needs to use.
• The TSA officer may have decided that you didn’t represent a threat, and therefore may have exercised discretion (which may or may not have been in keeping with the rules) to allow you to retain the solution.
• Re-reading your question, I note that you don’t say whether you actually discussed the contact lens solution with the officer when you were allowed to keep it. If you did not, they may simply not have noticed it. I’ve once or twice accidentally carried bottles of liquid through that the TSA screeners missed.
• If you did discuss the solution with the TSA, as I noted in my comment, it may just be that the TSA officer was not in the mood to argue, or that you are a particularly skilled negotiator. That’s kind of frightening, but it’s possible.

I do not know whether TSA rules allow laxer screening of domestic flights, but I doubt it.

I don’t believe that security should have allowed you to carry the contact lens solution on board on either flight.

In December 1994, Ramzi Yousef smuggled nitroglycerin on board Philippine Airlines flight 434 inside a bottle of contact lens solution, with other bomb parts concealed in his shoes, and assembled a bomb in the lavatory. When the bomb went off, one person died, another 10 were injured, and the plane almost didn’t make it back as the bomb damaged some control cables needed to fly the airplane.

(This is the same Ramzi Yousef who bombed the World Trade Center in 1993.)

As a result of this and some similar plots which failed, carry-on liquid containers are restricted in size.

To ensure that you get through security, you should bring a small bottle for use during your flight, and a larger bottle in your checked baggage.