Sure. While most constitutional monarchies extant today have relegated the monarch to a cultural icon with purely formal and ceremonial duties, a few strong monarchies, checked but not controlled by an elected body, still exist. Examples include the Kingdoms of Bhutan and Jordan, the Emirate of Kuwait, and the principalities of Monaco and Liechtenstein. In these countries, there is an elected representative and legislative body, however the monarchy retains key practical powers in the executive and/or legislative realms of governance, including presiding over lawmaking bodies, introducing legislation, veto power, appointing key government positions, etc. The model of the American President as chief executive has led to many nations retaining a monarch with similar power, while separating the legislative and judicial powers historically united under royal control.
One does have to recognize that this state of affairs is by its very nature a compromise, and historically speaking, most monarchs that have ceded lawmaking power to an elected body have seen that body use its power to further reduce the monarch's in cultural shifts toward popular government. Of the nations that recognize a monarch as head of state, most are former British possessions that recognize Queen Elizabeth II as their formal head of state, however their governments (most of them modeled on the Westminster parliamentary system) are totally self-sufficient and separate from that of the United Kingdom, and the Queen's role in these other countries is basically a face to put on money (if that). Most of the rest are Western European nations who have seen the monarchy reduced to cultural icon status in the wake of key disagreements between the monarchy and government that forced action.
The fate of the majority of monarchies in world history as of the beginning of the 20th Century were sealed by the spread of Communism in Europe and Asia, and the counter spread of Western-style democracy (or at least initially-deferential dictatorships) by the US and NATO in Central America and Africa; by the time the tides of the Cold War receded, most royal scions of the territories involved were deposed, dead and/or in exile, and the countries adopted various versions of an elected head-of-state/head-of-government, whether parliamentary or presidential.