Q:

How to allow same SKU for different products?

I need add same SKU for different product.
Example:SKU xyz-1 will be common for product_1, Product_2, and product_3

A:

From a practical perspective, you can't. A SKU is a unique field used to identify a product, the same way you can't duplicate an ID in a database.
Doing this will require a huge amount of work and it is highly not recommended. 

A:

As @mbalparda said, you cannot do this. Because, sku of a product should be unique. This is because Magento uses sku value in order to uniquely identify each product. So giving same sku id may produce unwanted behaviour. 
From your question, it is not clear why do you need same sku for multiple products . So I recommend you to leave sku attribute as it is and then create a new attribute for what you need to achieve. Let it be common_reference. Now set same value for those three products reference_1. Then use this attribute to do whatever you like to do. 
Hope that makes more sense

