如何在SQL中加入“备用”字段？

我具有以下表结构：

Table: products product_name, id_supplier, id_supplier_alt

Table: suppliers supplier_id, supplier_name

对于产品，我需要提取id_supplier和的供应商名称id_supplier_alt。

例如：

product_name | supplier_name | supplier_name_alt | apples | Store X | Store C | cherrys | Store Y | Store Z |

到目前为止，我已经尝试过：

SELECT p.products_name, p.id_supplier, p.id_supplier_alt, sup.name AS supname, sup.id_supplier AS supid, sup2.name AS supnamealt, sup2.id_supplier AS supidalt FROM products AS p LEFT JOIN suppliers AS sup on sup.id_supplier = p.id_supplier LEFT JOIN suppliers AS sup2 on sup2.id_supplier = p.id_supplier_alt

我得到的结果是错误的，当我检查该supidalt字段时，只是数字递增。知道我在做什么错吗？