My understanding is that to deepen a v-neck, is 1) you don’t connect in the round 2) and while knitting flat you continue to cast on new stitches for the neck-line ever x rows.
If you’re happy with the width of a sweater, how do you deepen the v-neck without making it wider? Is it fine to cast-on stitches for the neckline and then make decreases in the underam to net 0 extra stitches on the row?
I think I’d work out how many additional rows I wanted the v to end at and then adjust the increase rate at the neck so it began at the same width but increased less frequently.
If the increases are something like every 2 rows x number of times, then every 4 rows x number of times then every 6th row x number of times you could change one of the “every 2” to an “every 4” to lengthen by 2 rows, or change two of them to lengthen by 4 rows. You can also look at the different sizes in the pattern to see which area more or fewer increases are done at that frequency, for instance it may be best to keep the final increase or two as given and alter higher up on the v so that the base of the v sits nicely. I’d probably adjust the middle section.
The overall stitch count would be as per the pattern by the end of the v shaping even though it took more rows to get there.
I wouldn’t change the armhole shaping unless you’re unhappy with it.
Others may have different ideas of course.
Are you modifying a pattern or designing your own?
You might take a look at some free V-neck sweater patterns to see how they are worked.
Ann Budd has a wonderful book of sweater pattern templates in various styles, necklines and gauges. It’s very useful and may be in your public library.
https://www.amazon.com/Knitters-Handy-Book-Sweater-Patterns/dp/1931499438