Unfortunately, the crack of rifles and artillery pounding continued to the final tick of the tenth hour of the 11th month of 1918, resulting in almost 11,000 casualties on all sides on the final day, according to Joseph Persico. Famously, an American soldier rushed German lines a mere 60 seconds before the war's official end and was killed. However, I can find no mention of any large-scale offensives executed by the German army after the armistice's signing. Had one been ordered, it would have likely led to a wholesale revolt by German troops on the front.

At this point, the German Spring Offensives of 1918 sapped whatever strength German armed forces on the Western Front had left. Austria and the Ottoman Empire had already signed their own separate peace. Morale was dismal, and sailors of the High Seas Fleet, ordered to sortie out and fight in a last hurrah, mutinied, armed themselves, and seized the port of Kiel. The Kaiser, rightfully sensing the danger to himself, fled to Belgium. Chancellor to the Majority, Fredrich Elbert, was concerned that there would be a revolution if the Kaiser did not abdicate. Prince Max, the Kaiser's brother, begged the Kaiser to step down due to the very real possibility of an outbreak of civil war.

During this time, groups of troops and civilians in population centers protested in the streets, demanding an end to the war. Men on the front lines were still defending, as their duty compelled, but had little to no food, or ammunition, and were absolutely exhausted after throwing themselves at the allied forces in the Spring Offensive and the subsequent fighting and retreat during the Entente's 100 Days Offensive. One of the effects of the German Spring Offensives was to prove to the German Army they had been defeated as they overran allied lines and realized how well-supplied they were.

Entente forces, however, did continue to press the attack. General Pershing was completely against letting up and was called before congress after the war to explain why he had continued to press forward even after the Armistice had been signed. He replied, in essence, "I was ordered to." Marshal Ferdinand Foch issued an order on November 9th to all theater commanders to continue to advance until the armistice. General Pershing himself thought that the war should have been continued as he believed that armistice was a ploy to allow the German Army to reorganize.

So, to recap, while I know of no effort by the German Army to launch any large-scale offensives, I do know that Foch ordered the Entente commanders on the western front to continue offensive operations after the armistice had been signed. Had such an order been issued to German troops, it likely would have led to wide-spread rebellion.

References:

In the final hours of World War I, a terrible toll. (2018, November 9). The Denver Post. https://www.denverpost.com/2018/11/11/world-war-i-death-toll/

Keegan, J. (2000). The First World War. Vintage Books.

Persico, J. E. (2005). Eleventh Month, Eleventh Day, Eleventh Hour: Armistice Day, 1918, World War Iand its violent climax. Random House.