The idea of pursuit makes me imagine men running around with flashing red and blue lights in their pants.
That said, in terms of cultivating multiple relationships with women, some of which are intentionally non-platonic, need not be harmful, rude, or otherwise "bad". In fact, by showing the disconnect between interest and possessiveness/constraint, such men often are seen as more desirable. The same is also true of women – and it's not a strictly heterosexual phenomenon, for that matter.
Whoever you are, whatever your preferences may be, by showing a matter-of-factness in your interest in another that does not single them out too soon, you're showing maturity and comfort in your own sexuality and romantic relationships generally. This is, for the most part, a good thing – though the number of people who do this in a self-aware manner, with an equally self-aware partner are few and far between.
As with all relationship matters, rather than looking at the situation you perceive and filling in the rest with assumptions, it's best to express your feelings, and genuinely listen to what your partner/prospect has to say – and hopefully, move forward together in a manner that promotes mutual enjoyment and communication.
How do girls feel about it when guys pursue more than one girl at a time?