Sure, You can work on a new layout/design in your stage before pushing to live, essentially you'd just have two skins the existing one and the new one, you'd just need to make sure your dev on the new skin/components doesn't have a knockon effect on the existing skin/layout in case your planning on pushing any updates to the existing site whilst still doing dev on the new one.
Ideally you'd go into a change freeze. Its also possible to have two different looks n feels on the same live community this is often used when people have a B2B & B2C community or a customer community and staff community on the same instance.
Hope this helps
@madhukar1100 - Absolutely, you can do whatever you want with the layouts. There are many out of the box layouts available and then you can also override the available ones and also create new ones from scratch according to your requirements. Here are few articles available on how to actually achieve this.
I hope this helps.
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