Stoop Problem - Brownstone Patch?

Last winter, two small sections of the our front stairs/stoop began to give way. One of the problem sections is on the first stair and makes it hard to ascend. I understand the cost of re-brownstoning our stoop would be north of $5k. Apparently, the work was done by the previous owner only a few years ago but the new stone was not sealed. I have been hoping to have someone patch the 2 problem areas. Picture attached. At least two contractors have said that is not possible and suggested the entire stoop needs to be re-done. Does anyone have any ideas? I would be open to a short term solution to get through the winter but would really like to know whether a concrete patch or something similar is feasible. Any insight appreciated. Thanks all!