Yes, Argentina does allow for dual citizenship. But it is important to realize that those with dual nationality are recognized as citizens of Argentina only within Argentine territory. They need to enter Argentina by the use of an Argentina passport. But if they are entering for less than 90 days, they may enter using a foreign passport. When an Argentine citizen accepts the citizenship of another country, it must only be countries that allow them to keep their Argentine citizenship.
There are countries that do not allow them to keep the citizenship of other countries. They will be required to renounce their foreign citizenship as soon as they take on the other national citizenship. There is also a technical issue that Argentine citizenship is seen as a human right in many Supreme Court rulings and cannot be renounced. Thus, many countries wave the demand of renouncing their original citizenship if such rules are there