USCIS rarely denies an O or P petition outright. If it has concerns, it will send a Request for Evidence. If it then decides to deny the case, it may issue a Notice of Intent to Deny, if the decision will be based on information not submitted by the petitioner, or simply a Notice of Denial that will inform you of certain rights of appeal. As a general rule, appeals take too long and are expensive. Instead, if you feel you have a meritorious case, consider re-filing the petition as a new case (though you should inform USCIS of the prior denial and file number).

At least with USCIS, an appeal is theoretically possible. Remember that no such appeal is available at the next stage of processing if a consulate issues a visa denial, except if the consulate has erred as a matter of law, which they rarely do. Nor is there an appeal from decisions to deny entry by U.S. Customs and Border Protection (CBP).