Release duplicate versions of SAAS product?

I have an SAAS product that competes with a number of others.
I thought of an idea to create a duplicate product, that does exactly the same thing but with a different name and look-and-feel (the code can stay the same) - that way, i'll have 2 products competing for customers, which look like different companies but are the same.
What are your thoughts?

The question here is why one would do that?

That is a common strategy to focus on two distinct markets, for instance, high end and low cost.
If you go that road, I think you should not just change the "wrapping paper", i.e., don't just change the design and the domain. That approach can create very negative opinions when a customer finds out that he's paying extra for the same product of the same company.
Plus, you can do this through packages: "gold package" has it all; "silver package" has a bit less functionalities; etc. ...

That may be a strategic approach if, for instance, the low cost solution is a striped down version.
I remember that some years ago there was a voip company that had distinct "companies", they all had similar prices for land lines, but one was cheaper for US, other was cheaper for Europe. You could not use both with the same user (email used for authentication), because when you tried to register on the second solution they detect that you were already registered. (Obviously one could give a second email address...)

The point here is "why should you do it"? Will it have competitive advantages for your business? Is it part of some kind of strategy?

I think the idea is that google results won't fill up the first page of results with all pages from one domain, no matter how good your SEO is.

Since most people don't go past the first page, having 2 companies showing up when someone searches for "blue widgets", for example, doubles the chances of grabbing that customer rather than a competitor.

You can still charge exactly the same price for both "products"