SQL Server variable size and increase it

When you define a maximum size explicitly, then you cannot define higher than CHAR(8000) / VARCHAR(8000) or NCHAR(4000) / NVARCHAR(4000).

When you define a variable as CHAR(max) or VARCHAR(max), you set the maximum size of that variable to 2GB.

There is no way to define a variable with a maximum size between 8000 bytes and 2GB.