Combine the outputs of a sub model intermediate layer and a parent model

Question

I am trying to make a toy example work; there is a simple submodel:

Model: "sub_model"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 sub_middle (Dense)          (None, 100)               12900     
                                                                 
 sub_last (Dense)            (None, 100)               10100     
                                                                 
=================================================================
 

which is embedded in a parent model:

Model: "model"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 sub_model (Sequential)      (None, 100)               23000     
                                                                 
 last (Dense)                (None, 2)                 202       
                                                                 
=================================================================

Is it possible to create a third model which outputs the sub_middle layer's output and the parent model output?

Motivation: The sub-model can be a CNN predefined neural network e.g. VGG, with a custom head that is implemented in a parent model. I would like to create the third model for calculating the gradients of an arbitrary layer in the CNN predefined neural network in relation to the parent output.

The example code:

import tensorflow as tf
import numpy as np

sub_model = tf.keras.Sequential([
        tf.keras.layers.Input(shape=(128)),
        tf.keras.layers.Dense(100, name = 'sub_middle'),
        tf.keras.layers.Dense(100, name = 'sub_last'),
    ],
    name="sub_model",
)

model = tf.keras.Sequential([
        tf.keras.layers.Input(shape=(128), name = 'input'),
        sub_model,
        tf.keras.layers.Dense(2, name = 'last'),
    ],
    name="model",
)

# Works fine
grad_model = tf.keras.models.Model([model.get_layer('sub_model').input], [model.get_layer('sub_model').get_layer('sub_middle').output]) 

# Works fine
grad_model = tf.keras.models.Model([model.input], [model.input, model.output])

# ValueError: Graph disconnected
grad_model = tf.keras.models.Model([model.get_layer('sub_model').input], [model.get_layer('sub_model').get_layer('sub_middle').output, model.output])