The advice given to me was to go for rate and the multipliers will take care of themselves.
Even if your goal is to spend a fair amount of time running, there sill be times when you get bumped off your run frequency or you are looking for a run frequency or you are warming up or winding down and can spend some time doing search and pounce. During these time you can still go for rate but how long you wait in pileups might be guided by whether it's a new multiplier or not.
Exactly how much time to spend on these is operator dependent, but you can game it pretty easily with a spreadsheet.
- Take your rate running, say 100 QSOs / hour
- Take your rate cherry picking S&P, say 35 QSOs / hour
- Take your rate banging rare multiplier DX, say 12 / hour
And graph that in a spreadsheet based on your current totals. It changes over time, at the beginning, multipliers don't mean much, you give up 8 QSOs per S&P multiplier and it doesn't move the score much. Later on, when you have 1300 QSOs, that multiplier is worth a rare DX costs 8 (rounding down) QSOs
For instance, using the rates above, say you have 1300 QSOs and 80 multipliers. Your score is 104000. If you go for one more multiplier, you are at 1301 * 81 = 105381, versus continuing to run, 1308 * 80 = 104670 a difference of 741 points.
Of course, as time goes on, new multipliers are harder and harder to get so that rate goes down. This is where graphs are handy you can plot this all out with your rates as you go and that will tell you when to switch. You can also add rate goals to your spreadsheet and things that will help you notice when a band is becoming unproductive and it may be time to switch bands or take a break.