If I am reading your question right, then the answer to your question is yes. The reason being is that there it is highly doubtful the two non tandem breakers will be carrying full and constant loads at the same time. Of course you have to use the non-tandem breakers properly and not be using a 240V load off of them just 2 - 120V loads. This is set up to prevent overheating and damage to the bus. I am sure the manufacturer has "crash tested" these scenarios and that's why they have a restriction.
Added for clarity see comment.
I always try and use the contributors vernacular rather than trade nomenclature since it tends to confuse people. So let scrap that and insert some definitions.
- A panel is divided into pole spaces.
- A full size breaker takes up one pole space and service a 120V circuit.
- A two pole breaker takes up two spaces and if it serves a 240V circuit the poles are interlocked mechanically or internally.
- A half size breaker serves either two single 120V circuits or one 240V circuit in a one pole space. This is sometimes referred to as a tandem or piggyback breaker. (see the confusion).
You ITE Panel states that you shall not connect two pole breakers opposing each other (one on the left side and one on the right) in the panel, if the overcurrent protection adds up to 110A.
So I believe you question is can I install one two pole breaker and two one pole breakers in opposition even if they add up to over 110A? And my answer is Yes because if for no other reason it doesn't say you can't. For further explanation I tried to explain that the reason was to prevent overheating and damage to the bus.
I also tried to explain that you can not use this as a go around to install two, two pole breaker beside each other and then just remove the mechanical tie and say "Hey its really just two single pole breakers". Which by the way violates other code rules.
I am not sure what you meant in your comment about drop. I can tell you I am not talking about voltage drop. I am talking about overloading which will burn up the breakers and bus in you panel, and I am pretty sure that is what ITE has in mind also.
Hopes this helps