The play starts with a major plot, Orsino wooing Olivia. Orsino has been asking Olivia to accept his love, but Olivia refuses it. To woo Olivia, Orsino sends messengers to speak on behalf of him. This is the reason why Viola is dragged in the middle of this plot.
After being shipwrecked, Viola thinks that her twin brother Sebastian is dead. So in order to survive, she goes to work for the Duke. Orsino favors Viola (who is disguised as a male; Cesario) and sends her as a messenger to Olivia.
If Orsino had not sent Viola as a messenger to Olivia, Olivia would have never fallen in love with Viola (thinking she was a male). Since Olivia decided to pursue her love she mistakenly goes and marries Sebastian. This is the main reason why Viola gets to meet her brother again.
Sebastian and Viola looking for each other is an under plot. And it is because of the major plot this plot took place. This is how these two plots are interlinked. If one had not taken place, the results would not have been as effective as it is.
Another major plot is the trick played on Malvolio by Maria. This is not directly connected to the major plot, but one thing that made the trick easier was of its connection to one of the characters involved in the major plot. Malvolio believed Olivia loved him.
This fact is what the plot is based on. Malvolio is made into a fool by forging a letter from Olivia and Malvolio being arrogant believes the letter. This plot perfectly brings out everyones true character.
The locking up of Malvolio in the dark room and Feste disguising himself as Sir Topas has no connection to the major plot. This plot leads to the marriage of Maria and Sir Toby and the plot has its significance in the play on its own. How ever, Shakespeare has not secluded the whole plot from the play. We find a lot of connection between the characters in the se two plots. It is actually what this plot does.
The plot whish has more connections to the major plot is when Sir Toby and Fabian stirs up the fight between Viola and Sir Andrew. The reason is strongly linked to the major plot. Sir Andrew is in love with Olivia and when he notices Olivia paying more attention to Viola, Sir Andrew feels jealous. Tugging at this jealousy, Sir Toby and Fabian encourages Sir Andrew to fight Viola. This fight leads to Viola to believe that Sebastian is alive. This contributes to the under plot.
The various love themes are the major contributions to the plots. Without these love plots, the major plot and the under plots would not have been connected this strongly.
Every plot is connected to each other very effectively. In one way or the other, each incident or dialogue is linked and this is what completes the play.