Is it proper to have consecutive adverbs?

Is it proper grammar to have consecutive adverbs in a sentence?

e.g. "It was not exactly accidentally....

My thought is that is probably is not proper, especially in this case. The above could have been rewritten, "It was not exactly accidental...".

There are plenty of circumstances in which consecutive adverbs occur.

Using the adverb combination of OP's example, one could form a sentence like Though Sarah's pregnancy came as a surprise to many, it was not exactly accidentally achieved.

Other more common double-adverb constructions include phrases in which an adverb like very or rather precedes another adverb.

It is fine to write for example

It was not exactly accidentally done.

This means it is not exactly true that it was accidentally done.

As John suggests, ‘proper grammar’ is a chimera. We can draw conclusions about language only on the evidence of what actually occurs in it, and consecutive adverbs certainly do occur. The locus classicus could well be (my emphasis):

I'll be your dream I'll be your wish I'll be your fantasy.

I'll be your hope I'll be your love be everything that you need.

I'll love you more with every breath truly madly deeply.