In such cases you need a strategy. How many stitches to cast on and how many stitches to increase is a question of tactics. But a general plan, that is, what should be done and in which sequence, constitues strategy. First, you can always start from the collar but recently I would rather knit the whole sweater and deal with the collar afterwords. In this case you get a sence of proportions from the very beginning. Of course there are exceptions when you start from the collar but for the sake of simplicity I am not discussing this now. There are several possible solutions: (1) increase stitches; (2) switch to thicker needles; (3) to knit the collar from a heavier yarn, for instance, the main yarn held double. You can combine these options. Most frequently I use (1) and (2). Sometimes it is enough to switch to thicker needles several times (I recommend going at once 0.5 size up). But this solution is not universal, it depends on the yarn. In this case you can at first make some increase rounds or to increase in the beginning and then to switch to thicker needles.
As you see, the collar has a shape of trapezium. It is of this sweater:
Mostly I do the following. I knit 5-7 cm, then increase by 20-25 % and knit some 10 cm more, then switch to thicker needles. In the next issure of Käsitöö there will be two sweaters with a large collar, so you can study the particular patterns.