Edit polygon coords using Python, Shapely and Fiona

I need to edit the geometry of intersecting polygons and I don't know how I can save modified geometry to a shapefile. Is it even possible?

from shapely.geometry import Polygon, shape
import matplotlib.pyplot as plt
import fiona


c = fiona.open('polygon23.shp', 'r')
d = fiona.open('polygon23.shp', 'r')

for poly in c.values():
    for poly2 in d.values():
        p_poly = shape(poly['geometry'])
        p_poly2 = shape(poly2['geometry'])
        intersect_polygons = p_poly.intersection(p_poly2)
        if type(intersect_polygons) == Polygon:
            intersect_polygons = p_poly.intersection(p_poly2).exterior.coords
            if p_poly.exterior.xy != p_poly2.exterior.xy:

                y_difference = abs(intersect_polygons[0][1]) - abs(intersect_polygons[2][1])
                
                coords_polygonB = p_poly2.exterior.coords[:]
                
                coords_polygonB[0] = (coords_polygonB[0][0], coords_polygonB[0][1] + (y_difference))
                coords_polygonB[1] = (coords_polygonB[1][0], coords_polygonB[1][1] + (y_difference))
                coords_polygonB[2] = (coords_polygonB[2][0], coords_polygonB[2][1] + (y_difference))
                coords_polygonB[3] = (coords_polygonB[3][0], coords_polygonB[3][1] + (y_difference))
                coords_polygonB[4] = (coords_polygonB[4][0], coords_polygonB[4][1] + (y_difference))
                
                p_poly2 = Polygon(coords_polygonB)

                x,y = p_poly.exterior.xy
                plt.plot(x,y)
                x,y = p_poly2.exterior.xy
                plt.plot(x,y)
                plt.show()

from Edit polygon coords using Python, Shapely and Fiona