In this SparkNote, it mentions that Don Pedro "seems to have no romantic interest of his own," although in Act 2, Scene 1 (beginning around line 275) Don Pedro is talking with Beatrice about her views on marriage after the masquerade. Beatrice makes a joke, saying, "I would rather have one of your father’s getting. / Hath your grace ne'er a brother like you? / Your father got excellent husbands, if a maid could come by them." Don Pedro responds, "Will you have me, lady?" which is potentially another joke, although it may also be quite a serious question (The 1993 film version of the play, directed by Kenneth Branagh, takes the more serious approach, for example). If Don Pedro is serious in this question, it may also add to the reasoning for Don Pedro's melancholia at the end of the play. Being infatuated with Beatrice, her engagement to Benedick would certainly add to (or perhaps even be the main cause for) his melancholia. If the play is presented in a way that places significance on Don Pedro's response to Beatrice, he clearly does show romanic interest in the play.