A rough inference of purity is potency (% of EPA/DHA per gram). 50% is not bad.
I agree that more is not alway better, even with my most loved fish oil. But if you are increasing the amount for a specific reason (e.g. improve asthma) then it can be warrented. If I were you would I move up to six grams EPA/DHA to see if it improved my asthma, yes.
The data with EPA/DHA and asthma is far from conclusive but it is suggestive (wow that was a vague statement!). You would notice the difference much sooner than 4-6 months. Red Blood cell levels of EPA/DHA can equilbrate in as little as 4 weeks (4-6wks is the range found in the literature). So I would imagine that if you were going to see a difference then you would see it by then.
Keep a journal so monitor the status of your asthma (inhaler use, frequency of chest tightness, response to exercise, etc) as that will be the marker of improvement in this situation.
Again...check with your doctor
-MR