This is best asked by way of example. Suppose I want to ask someone if they have done some action, or plan to do so. And to be precise, suppose either is acceptable to me. So I might ask:
Have you painted the house, or do you plan to paint it?
But I could make that more succinct as follows:
Have you, or do you plan to, paint the house?
Now I prefer the latter, but it has a problem to my eyes/ears in that the tense of the verb "paint" now agrees only with the "plan to" in the interrupting clause. That is, it does not agree with "Have you" at the start, which really wants "painted".
As a result, in this particular situation, I simply wouldn't use the second version even though, as I say, I prefer it. There are numerous examples where this agreement problem does not arise in which case I'd use it. For example:
Do you plan, or have you simply decided not, to paint the house?
Am I being overly cautious? For example, is there perhaps a rule that says my second version is OK -- e.g. maybe the rule is that the verb's tense need agree only with the last of a sequence of verbs?
Finally, a similar question. In the second example I give above, where I show a situation where tense agreement is not a problem, is what I gave:
Do you plan, or have you simply decided not, to paint the house?
is better or worse than:
Do you plan to, or have you simply decided not to, paint the house?
As a computer programmer, I prefer the first because it demonstrates better re-use, but using programming practices to guide English use is not always a good idea :-)