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In an advanced Search, when search Type is selected to "All Types", it is resulting only the common Attributes(Created On, Last Modified, Name, Number) under Criteria section as shown below,
Above is the default behaviour, but our requirement is to get the Attributes of all object Types under Criteria, on selecting a search Type as "All Types"
That just seems to be by design, in that if you pick "All Types", it's only going to include criteria common amongst those types, to use as search criteria:
We document it, as such:
I don't think there is any way around this, to get your desired behaviour, without a product change, so you could try posting a product idea (but that would involve a design change in the product).