[Tryst]

Personally I don't use buy-stops and don't know many that do on here as you have a much higher risk of a false breakout, but one suggestion that might be of use is to set up alerts, that will be triggered when a price level you are watching is reached instead, as that way you can enter a partial position manually once you've checked the chart, and then monitor it until near the close, which if still strong and hasn't run too far above the breakout level then you can do additional buying as Weinstein said in his answer.

A question, when you say 'if a stock hasn't run up too far...after monitoring it near the close...' are you implying that if a stock has a surge on increasing volume and never returns back during the day of breakout, then an opportunity is missed? Only stocks that don't breakout aggressively during the day of breakout, but do stick a landing/close above the breakout level should be invested in?

A great chart to look at which had a breakout on strong volume, with a low volume retracement to support (prior resistance) and then a breakout after a retest of support is LSE:FCCN.