I hope I understood your question correctly -
1) One table can not have more then one primary key.
create table User(
name TEXT NOT NULL ,
email TEXT NOT NULL ,
PRIMARY KEY (email)
);
2) Its possible to have one primary key and rest as keys (unique key).
create table User(
name TEXT NOT NULL ,
email TEXT NOT NULL ,
PRIMARY KEY (email),
KEY (email)
);
3) Its also possible to have a combination of two column as a single primary key where individual value can be repeated in the same table but not the combination
create table User(
name TEXT NOT NULL ,
email TEXT NOT NULL ,
PRIMARY KEY (name, email)
);