Oracle PL/SQL - Raise User-Defined Exception With Custom SQLERRM

Is it possible to create user-defined exceptions and be able to change the SQLERRM?

For example:

DECLARE
    ex_custom       EXCEPTION;
BEGIN
    RAISE ex_custom;
EXCEPTION
    WHEN ex_custom THEN
        DBMS_OUTPUT.PUT_LINE(SQLERRM);
END;
/

The output is "User-Defined Exception". Is it possible to change that message?

EDIT: Here is some more detail.

I hope this one illustrates what I'm trying to do better.

DECLARE
    l_table_status      VARCHAR2(8);
    l_index_status      VARCHAR2(8);
    l_table_name        VARCHAR2(30) := 'TEST';
    l_index_name        VARCHAR2(30) := 'IDX_TEST';
    ex_no_metadata      EXCEPTION;
BEGIN

    BEGIN
        SELECT  STATUS
        INTO    l_table_status
        FROM    USER_TABLES
        WHERE   TABLE_NAME      = l_table_name;
    EXCEPTION
        WHEN NO_DATA_FOUND THEN
            -- raise exception here with message saying
            -- "Table metadata does not exist."
            RAISE ex_no_metadata;
    END;

    BEGIN
        SELECT  STATUS
        INTO    l_index_status
        FROM    USER_INDEXES
        WHERE   INDEX_NAME      = l_index_name;
    EXCEPTION
        WHEN NO_DATA_FOUND THEN
            -- raise exception here with message saying
            -- "Index metadata does not exist."
            RAISE ex_no_metadata;
    END;

EXCEPTION
    WHEN ex_no_metadata THEN
        DBMS_OUTPUT.PUT_LINE('Exception will be handled by handle_no_metadata_exception(SQLERRM) procedure here.');
        DBMS_OUTPUT.PUT_LINE(SQLERRM);
END;
/

In reality, there are dozens of those sub-blocks. I'm wondering if there's a way to have a single user-defined exception for each of those sub-blocks to raise, but have it give a different message, instead of creating a separate user-defined exception for each sub-block.

In .NET, it would be sort of like having a custom exception like this:

    public class ColorException : Exception
    {
        public ColorException(string message)
            : base(message)
        {
        }
    }

And then, a method would have something like this:

        if (isRed)
        {
            throw new ColorException("Red is not allowed!");
        }

        if (isBlack)
        {
            throw new ColorException("Black is not allowed!");
        }

        if (isBlue)
        {
            throw new ColorException("Blue is not allowed!");
        }