I would consider the deal that Antonio and Shylock make, in which Shylock lends Antonio money under the condition that Antonio surrender a pound of flesh should he not pay it back in three months time, the main plot driving the action of the play, not a subplot. The three subplots are as follows:
The casket plot: in this subplot, Portia cannot chose her suitor but must marry whoever picks the right casket, according to instructions left in her father will.
Lorenzo and Jessica's elopement: Shylock's daughter Jessica elopes with Antonio and Bassanio's friend Lorenzo, enraging Shylock.
The ring plot: both Portia and Nerissa, in disguise, demand the rings that Bassanio and Gratiano promised never to part with.
The three subplots are connected because they all involve love. Portia, for example, complains to Nerissa that she cannot chose her own husband. Although she ends up with the man she wants, this subplot critiques patriarchal control over women: Portia amply demonstrates when she successfully defends Antonio that she has the intelligence and judgment to choose her own mate. Jessica also resists patriarchal control when she defies her father to run off with the man she loves. Portia and Nerissa demonstrate their love, mercy, and forgiveness towards their lovers when they return the rings the lovers gave away.
All three subplots are also strongly connected with Belmont, Portia's home of enchantment and romance outside Venice. The casket plot takes place at Belmont, Jessica and Lorenzo end up at Belmont, and Portia and Nerissa return the rings at Belmont. This place of love is a contrast to Venice's mercantilism and commerce.
As the other educator has pointed out, it is widely agreed that the three subplots within Shakespeare's Merchant of Venice are (1) the romantic pursuit of Portia by suitors who have to win her through the appropriate choice of casket, (2) the contract made between Shylock and Antonio on peril of "a pound of flesh," and (3) Portia's disguising herself in order to defend Bassanio and the subsequent deception surrounding the ring.
All three subplots are tied together by the presence of Bassanio and the theme of deception. In each subplot, not all is what it seems to be. In the first one, Portia's other suitors pick the more glamorous caskets (the gold and the silver ones) and it turns out that Bassanio's less fancy choice (the lead casket) is the correct one. In the second subplot, Shylock enters into the contract with Antonio (who is supporting Bassanio) knowing that he can use it as vengeance for the longstanding grudge he's been nursing. In the third subplot, Portia dresses herself as an attorney and tricks Bassanio into giving up the ring he had promised not to give away.
Most critics believe that there are three subplots to Merchant.
1. The casket plot for Portia's suitors.
2. The bond/contract plot between Antonio and Shylock.
3. The ring plot between Portia and Bassanio and Nerissa and Gratiano.
The plots are interconnected not only through characters but...
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also through themes.
1. Portia wants Bassanio to choose the right casket so that she may marry him.
2. Bassanio's connection to the casket plot links him to the bond plot. If he did not need to borrow money from Antonio to impress and woo Portia, Antonio would not have entered into the bond with Shylock.
3. The ring plot does not develop until Act 4 (the trial scene). Portia argues for Antonio's and Bassanio's sake against Shylock and in saving Antonio's life eventually requests her ring back from Bassanio.
Through Bassanio, the subplots are connected. Thematically, the plots share a connection. The casket plot expresses the truth that appearance does not always equal reality. The ugliest and seemingly worthless lead casket possesses the prize. This theme of misleading appearances continue in the bond plot. For example, Shylock believes that his bond is airtight, that Antonio has no escape, but Shylock doesn't look below the surface of his "pound of flesh" request. Likewise, Portia disguises herself as a man to resolve the bond plot. Everyone believes her to be a young, gifted lawyer, but the audience knows who she really is. Finally, the ring plot also demonstrates appearance versus reality. Portia, dressed as a man still, manipulates Bassanio into giving her the ring that he promised never to remove. In the end, Portia teachers her new husband that all is not as it appears by disclosing her involvement in the trial and her repossession of the ring.