You could mean you want to increase every existing value that you already have in a number field by 1. That is one thing.
I think you want the next number that is one higher than the highest one you already have in that field. That is another thing.
If they are going to be successive anyway, what's wrong with using an autonumber since it already does what you are trying to do? What you're suggesting is no more reliable and could cause data integrity issues if the last record is deleted. The next record will have the same highest number that you had before, but there might be records related to the old record with that same number.
Then there is the issue of when are you going to create this number? If you need it at the beginning of a process because of form/subform relationships, you will have a Pandora's box that you don't want to open, especially in a db with concurrent users. Nasty things can happen, especially if someone starts then cancels a process while someone else completes it. At the very least, your number sequence will no longer be sequential, and if this is your objection to the autonumber type, you need more understanding of what exactly these are for.
If I've missed the mark and you still want to do this, the answer might be a simple function or maybe an Append query that has a calculated field.