I believe edits are encouraged over duplicate questions.
If you did have two questions (or more depending on how many suggestions you get), at best you're splitting attention across a bunch of similar questions and at worst they're getting closed as duplicates and you're losing rep. Remember that people will still be running into your original question, and they won't know that the answers already provided haven't worked.
Moreover, updating your question helps the people already answering as they will see the new information and might have more ideas. It also shows that you are engaged in getting an answer rather than shooting off a bunch of questions and then vanishing quietly.
Also remember, by editing your question, you'll be bumping it back to the top of the question list, so even more people might see it.