It is already possible in Mandelbulber. Below are setting for morphing between Mandelbulb Power 2 and Julia set with C=(-1, 0, 0)
It is made as a hybrid fractal.
In first slot there is main fractal formula (Mandelbulb Pow 2), but with "Don't add C constant" enabled.
In second slot is addition of C constant depending on pixel position
In third slot there is addition of Julia constant
Morphing is done by adding weight values for second and third slot to animation table. By decreasing weight for second slot and increasing weight for third slot there is made morphing between Mandelbrot and Julia sets.

# Mandelbulber settings file
# version 2.16
# only modified parameters
[main_parameters]
ambient_occlusion_enabled true;
camera -2,130999575970423 -2,659811253990262 0,7890643249307752;
camera_distance_to_target 3,218288059286709;
camera_rotation -31,51667761363774 -14,19255329033587 0;
camera_top 0,1281677670855954 0,2090141986028645 0,9694772242103962;
check_for_bailout_2 false;
dont_add_c_constant_1 true;
flight_last_to_render 0;
formula_1 3;
formula_2 1007;
formula_3 1001;
formula_weight_3 0;
hybrid_fractal_enable true;
keyframe_last_to_render 0;
mat1_is_defined true;
mat1_specular 4;
mat1_specular_width 0,063;
raytraced_reflections true;
target -0,5 0 0;
[fractal_1]
power 2;
[fractal_2]
[fractal_3]
transf_addition_constant -1 0 0;
[keyframes]
frame;main_camera_x;main_camera_y;main_camera_z;main_target_x;main_target_y;main_target_z;main_camera_top_x;main_camera_top_y;main_camera_top_z;main_formula_weight_2;main_formula_weight_3
0;-2,130999575970423;-2,659811253990262;0,7890643249307752;-0,5;0;0;0,1281677670855954;0,2090141986028645;0,9694772242103962;1;0
1;-2,130999575970423;-2,659811253990262;0,7890643249307752;-0,5;0;0;0,1281677670855954;0,2090141986028645;0,9694772242103962;0;1
2;-2,130999575970423;-2,659811253990262;0,7890643249307752;-0,5;0;0;0,1281677670855954;0,2090141986028645;0,9694772242103962;1;0
interpolation;morphAkima;morphAkima;morphAkima;morphAkima;morphAkima