Although you are purifying the enzyme, each step of the purification is not perfect. At each step you will lose some enzyme, but the hope is that you will lose many more of the contaminants. Certainly during a purification, you should not see an increase in the total amount of enzyme activity, because that would suggest that enzyme is appearing out of nowhere (or, perhaps more realistically, you are purifying the enzyme away from some inhibitor).
In general, when designing an enzyme purification strategy, you need to balance yield (how much enzyme you get out in the end) versus purity (how few contaminants there are). In general, adding more purification steps will decrease the yield but increase the purity.