While it is valid, it would be considerably rarer than placing the not before the to:
It splits the infinitive. Now, the "rule" against splitting the infinitive is of course utter nonsense, but there are still people out there who believe in it and so they would avoid it, and one might as well follow suit when it makes no difference, rather than have to defend one's choice.
Also, while it is not a matter of a rule, keeping the infinitive together is the more common pattern even by those of us who know we've the option of doing otherwise.
However, it's also common to have the to appear after a verb. Consider:
I hope not to meet them until I am better prepared.
I hope to not meet them until I am better prepared.
In this case the meaning is pretty much the same. The first would be preferable to a no-split-infinitive stickler, but the second certainly seems more natural to me in the "[verb] to" pattern.
There can also be a difference in just what is negated.
I played, not to win.
"I played, but winning was not my goal, but I wouldn't have objected winning" or "I played, with not winning as a goal". We could argue the second meaning, but the first seems the much more likely meaning.
I played to not win.
"I played, with not winning as a goal" seems the only possible interpretation.
Often though, the forms would be equivalent. "To be or not to be" wouldn't differ in meaning from "To be or to not be"; any subtle difference in what is logically meant amounts to the same thing. Since there's no reason to favour the latter such as the previous examples quote, the not seems unnecessarily emphasised in the latter, just by dint of not being quite where we might expect it.
As used in your dictionary, there are two good reasons for favouring the "to not [verb]" pattern:
- It is closer to the "to not win" example above, in that the negative is a stronger part of the meaning.
- The gloss is contracted to a case where the infinitive stands as a phrase on its own. In this relatively rare case, generally only found with definitions, we want to just have the "to [verb]" but since we need to negate the verb, this becomes "to not [verb]" to remain with that pattern.
Since you said "ongoing", as an adjective, further could be used in the sense 'additional.'
The meeting ended without any plans for further discussions.
I would appreciate your considering my application further....
In the same vein, you could use further in your sentence, however, in my opinion a better construction will be:
I would appreciate your further consideration of my application
or
As @Joe states, 'I appreciate your consideration of my application
Further discussion
Best Answer
English does not always have at least two words in an infinitive. This is a common misconception, possibly resulting from the facts that
the to-infinitive form is met with far more commonly than the bare infinitive in common constructions
in the past, dictionaries would pick up on this, and give an entry for 'to swim' rather than 'swim' etc. This practice is happily falling off.
Examples:
I want to wash my hair tomorrow.
I didn't dare wash my hair in that new shampoo. (to optional here)
I helped wash the dishes. (to optional here)
So "I'd be happy to further assist you." doesn't split an infinitive but a to-infinitive.
That said, what about the practice of 'splitting to-infinitives'?
According to G. Pullum [ucsc.edu], this 'rule' is a myth:
Myth: You must never split an infinitive.
Pullum responds: Hemingway didn't write the phrase "to really live" by mistake; it is perfect English. "To" introduces infinitival verb phrases, and "really live" is an infinitival verb phrase (containing a preverbal adverb). Nothing is split in this form of words.