Ramayana & Mahabharata don’t overlap for just once. There was an incident when Krishna saved Arjuna’s life at the Rama Setu in presence of Hanumana.

Krishna once told Arjuna that Rama was the greatest warrior ever – even better than him. When visiting Rameshwaram, seeing the Nala Setu, a doubt arose in Arjuna’s mind. He wondered why Rama, who was supposedly the greatest warrior, needed the Vanara Sena to create the Setu, when he could have just created a bridge with arrows using his powers.
Hanuman found Arjuna engaged in such doubts and went up to him, disguised as an aged Vanara. He explained to Arjuna that the bridge of arrows would not be able to withstand the weight of the Vanars. Challenging Hanuman, Arjuna said that he would create such a bridge and if the Vanara could walk on it, he would win. Otherwise, he would burn in the bridge of arrows. After building the bridge with his powers, he asked the Vanara to walk on it. Hanuman uttered the name of Rama, and merely kept his tail on the bridge. The bridge collapsed.
Keeping his word, Arjuna burnt the bridge and turned to walk in it. That very moment, Krishna appeared in the form of a saint and asked them to perform the task again, with him as a witness. But this time, the bridge did not crumble. When they turned around, they saw that the saint was supporting the foundation of the bridge with his shoulders bleeding. In the saint, Hanuman saw Rama and Arjuna saw Krishna. Krishna hugged Hanuman and thanked him for what all that he had done for him.