It if often practical to use a common post and footing to support two or more beams in a deck design. This usually happens in multilevel decks where a lower deck intersects with an upper deck along a line of posts and footings. Stair landings that wrap around the frame of a deck often take advantage of sharing a corner post.
Although this can be a great technique for reducing your quantity of footings for your project you must be careful to consider the types of compound forces you will be exerting on the post. A beam attached to the side of a post will be pulling out and down away from the post. You must maintain a minimum 1-1/2" beam bearing ontop of a post. In order to satisfy this requirement you will need to create a notch in the lower section of the post. Installing a cleat along the post below the beam can provide added stability and increased support.
Consider how large amounts of load applied from the side coupled with the downward force of the higher beam can overload the capacity for the post and don’t forget to adjust your footing size to accommodate the additional loading. Be sure to use the proper type and quantity of fasteners to prevent them from shearing off under the load. Using long ½” carriage bolts will work well in this application. Check with your building inspector.