This is related to my previous question.
To apply amplitude amplification in Qiskit, one needs to use AmplificationProblem() or GroverOperator(). According to documentation:
$$\mathcal{Q}=\mathcal{AS_0A}^{\dagger}\mathcal{S_f},$$ $\mathcal{A}$ is an input state preparation. In the standard Grover search $\mathcal{A=H^{\otimes n}}$.
However, in generalized form, $\mathcal{A}$ to could be a circuit representing any (non-uniform) superposition of basis states.
So now imagine we have a circuit. One of the QuantumRegisters (qubits=[0,1,2]), is initialised in the superposition of $\{|0001\rangle, |0100\rangle, |0111\rangle\}$ states. The oracle and good_states have been both set to $|0111\rangle$.
good_state=['0111'] oracle_state_vector=[0]*(2**4) for index in [7]: oracle_state_vector[index]=complex(1, 0) oracle=Statevector(oracle_state_vector) testCirc=QuantumCircuit(4) initial_state=[1,4,7] init_state_vector=[0]*(2**3) normConstant=1/m.sqrt(len(initial_state)) for state in initial_state: init_state_vector[state]=normConstant*complex(1, 0) testCirc.initialize(init_state_vector, [0,1,2] ) testCirc = RemoveResetInZeroState()(testCirc.decompose()) state_preparation=testCirc #state_preparation.x([3]) problem = AmplificationProblem(oracle, is_good_state=good_state, state_preparation=state_preparation, objective_qubits=[0,1,2]) state_preparation.draw() backend = Aer.get_backend('aer_simulator') quantum_instance = QuantumInstance(backend, shots=1024) grover = Grover(quantum_instance=quantum_instance) result = None if problem is not None: result = grover.amplify(problem) print(result.assignment) if result is not None: display(plot_histogram(result.circuit_results[0])) The histogram shows we were able to amplify the amplitude of the $|0111\rangle$ state. 
However, if we add a X gate (by X I am trying to abstract part of a potential algorithm that can be applied on a QuantumRegister) to the other QuantumRegister,qubit[3], the amplification result is not satisfying anymore.
What am I missing here?
