Scenario: There's a job opening in your current company for a position two pay grades above you. It's the same generic job title, only it's a more senior position. You barely meet the job requirements but have a small advantage. You have some, say 3 years, of working directly and indirectly with the product/process/etc. which the job will be accountable for. This skill set associated with this product/process/etc. is in very high demand and low supply.
Does corporate policy tend to have an unwritten rule about "skipping" a job title, especially for entry level employees? Is that unwritten rule usurped by good, even great, results? Does the aforementioned scenario change these answers? Regardless of answer, in your experience, do you have any examples of a person getting (or not) that promotion? Is it potentially damaging to your relationships and/or future promotion prospects?
Think hard
If you can categorically meet the requirements for the role, apply. If not, I believe it could be potentially damaging to future relationships.
Regardless of any "unwritten rules", applying for a job you can barely do will either result in:
Can you do the job? Can you meet the deliverables? Can you demonstrate that at interview? Are your results in line with what's expected?