 Here is a Python code sample that demonstrates the use of the pydpf-core library for multi-stage cyclic symmetry analysis with advanced customization. Please note that you need to install the pydpf-core library before running this code.

```python
from pydpf_core import DPFLabFactory, ResultDefinition, ResultInfo, CyclicSupport, Sector, Mesh, Field, OutputsCyclicExpandedDisplacement, InputsCyclicExpandedDisplacement

# Initialize the DPFLabFactory
dpf = DPFLabFactory()

# Download a multi-stage cyclic result
dpf.should_start_server()
result_id = 'your_result_id'
dpf.download_multi_stage_cyclic_result(result_id)

# Create a model from the downloaded result
model = dpf.create_model()

# Get the model's state
model_state = model.get_state()
print(model_state)

# Verify that the model is a multi-stage model
if model_state.result_info.get_number_of_results() > 1:
    print("Model is a multi-stage model.")

# Get cyclic support
cyclic_support = CyclicSupport(model)
num_stages = cyclic_support.get_num_stages()
num_sectors_per_stage = cyclic_support.get_sectors_scoping()[0].get_num_sectors()
num_nodes_base_sector = cyclic_support.get_sectors_scoping()[0][0].get_num_nodes()
print(f"Number of stages: {num_stages}")
print(f"Number of sectors per stage: {num_sectors_per_stage}")
print(f"Number of nodes in the first stage's base sector: {num_nodes_base_sector}")

# Expand displacement results on chosen sectors
sectors_to_expand_stage1 = [Sector(0, 0)]
sectors_to_expand_stage2 = [Sector(1, 0), Sector(1, 1)]

# Create a displacement cyclic operator
displacement_operator = model.create_operator('Displacement')

# Expand the displacements and get a total deformation
expanded_displacements = displacement_operator.cyclic_expanded_displacement(sectors_to_expand_stage1, sectors_to_expand_stage2)
total_deformation = expanded_displacements[0] + expanded_displacements[1]

# Get the expanded mesh
expanded_mesh = model.create_mesh_and_field_mapped(total_deformation, Field.Displacement)

# Plot the expanded result on the expanded mesh
# (You need to use a plotting library like matplotlib for this part)

# Expand only some sectors for the mesh and plot the expanded result on the expanded mesh
# (You can modify the sectors_to_expand_stage1 and sectors_to_expand_stage2 variables to achieve this)

# Check results precisely
time_frequency_support = cyclic_support.get_time_frequency_support()
print(f"Time frequency support: {time_frequency_support}")

# Verify that the displacement values are the same on all nodes
for node in expanded_mesh.get_nodes():
    node_displacements = [sector.get_field_value(node, Field.Displacement) for sector in expanded_displacements]
    if len(set(node_displacements)) > 1:
        print(f"Displacement values are not the same on all nodes.")
        break

dpf.should_average()
```

This code assumes that you have a multi-stage cyclic result with the appropriate APIs available in the pydpf-core library. You may need to adjust the code according to your specific use case and the structure of your multi-stage cyclic result.