Symbolism, Imagery, Allegory
Whenever Common Man switches identities (which happens a lot), he pulls his latest costume out of the same handy basket he uses to set the stage for the next scene. This not only allows A Man for All Seasons to transition between settings in a graceful way, but it also allows Robert Bolt to comment on the nature of theater as a whole.
A Basket For All Seasons
First off, Common Man's basket contains the settings for scenes. These are typically small objects, like a book or a candle, but they go a long way toward signifying the different locations of the play. This is further amplified by the monologues that Common Man delivers while setting the stage, which typically take into account future historical context; we get the sense that Common Man exists on a different plane of existence from the other characters.
In addition, Common Man pulls his various costumes out of that same handy basket. Usually, this takes the form of hats that represent the various professions he fills throughout the play, such as a boatman or innkeeper. Ultimately, we see these costumes all come together as Common Man sets the stage for More's trial:
([...] He brings it on the jury bench, takes hats from the basket and puts them on poles with a juryman's hat, takes jailer's hat off head and puts it on a pole. Seven are plain gray hats, four are those worn by the STEWARD, BOATMAN, INNKEEPER, and JAILER.) (2.680)
This is a unique occurrence in the play: Common Man is using his basket to fulfill both of its purposes simultaneously—defining characters and setting the stage for scenes.
A Night at the Theater
We also have to think about the theatrical effect of Common Man's basket. A Man for All Seasons is pretty heavy on stage direction, and you could imagine the play feeling quite different if it had traditional scene changes. So why did Bolt choose to go with Common Man and his basket? We can't say for sure, but we'd argue that Common Man—and his basket—go a long way toward grounding the audience and providing it an easy pathway into the distant world that the play depicts.
While it isn't a symbol in the traditional sense, Common Man's basket is a unique theatrical device that defines A Man for All Seasons. Whether you see it as a clever way for Bolt to provide historical context or a clever way for him to comment on the nature of theater, the basket is the glue that holds together the entirety of the play.