You can expunge all of them once your are off probation. There are several requirements of course, but mainly that you are not currently on probation for any of them (or anything else) and not currently facing new charges of any sort. The problem you face is that you likely had your probation violated on one of the 2007 DUIs when you picked up the 2nd one in 2007. If so, then the requested relief is discretionary by the judge and not mandatory. Definitely get an attorney to properly advise you and handle this for you.
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In theory, there is no limit. In general, you must be off of probation and have paid all fines and fees and restitution that might have been ordered. Hiring an attorney with experience in these matters will improve your chances of having the expungement applications be granted. Good luck.
If they are all misdemeanors then it is possible to have them all expunged if the court cooperates with you. If any of them were felonies you cannot have served any prison time on it for a charge to be eligible. I would consult with an attorney familiar with post conviction procedures. Good luck.
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The court has the discretion to expunge any misdemeanor upon a properly made motion. You should be aware that having a DUI "expunged' will not change your DMV record and the DUI convictions can still be charged as priors IF (and I'm sure you don't want to deal with this ever again) you get arrested again. Good luck.
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There is no limit of convictions which can be expunged. It is discretionary, however, and you will need to show the judge you have been rehabilitated. There is also an issue of you not remaining law abiding while you were on probation, but a strong showing of your efforts to reform will help. The DMV record will remain even after a court expungement.
At this point, all your 3 DUIs are priorable (if your 2003 DUI conviction was after June 2003). If before June 2003 then it is not priorable meaning if you pick up another DUI today, you will only have 2 priors as opposed to 3. For expungment, try to do the 2003 now and then in a few years try to get the other 2 expunged. Since you picked up 2 DUIs in 2007, even if you try to get it expunged, your motion will be denied. It all depends on the judge. Certain cities have liberal judges and they grant it and come cities don't. Good luck.