Setting the Stencil Test Function and Stencil Operation for subsequent draw calls in Unity SRP

Question

I'm using HDRP and I would like to extend it without actually modifying HDRP code or writting my own SRP.

I'd like to:

1. Render some objects with a custom shader
2. Have those objects increase a stencil value
3. Setup the stencil state for the next camera in the list so that the main scene only renders again when the stencil matches that value

Here's my pseudo-code:

using System.Collections;
using System.Collections.Generic;

using UnityEngine;
using UnityEngine.Rendering;
using RenderPipeline = UnityEngine.Rendering.RenderPipelineManager;

public class MyRenderTest : MonoBehaviour
{
    private ushort m_StencilValue = 0; // The scene is only rendered if the stencil equals to this value

    void OnEnable()
    {
        RenderPipeline.beginContextRendering += OnBeginContextRendering;
        RenderPipeline.beginCameraRendering += OnBeginCameraRendering;
        RenderPipeline.endCameraRendering += OnEndCameraRendering;
    }

    void OnDisable()
    {
        RenderPipeline.endCameraRendering -= OnEndCameraRendering;
        RenderPipeline.beginCameraRendering -= OnBeginCameraRendering;
        RenderPipeline.beginContextRendering -= OnBeginContextRendering;
    }

    void OnBeginContextRendering(ScriptableRenderContext context, List<Camera> cameras)
    {
        m_StencilValue = 0;

        // Unity clears the main stencil buffer before this call, so no need to do it ourselves
    }

    void OnBeginCameraRendering(ScriptableRenderContext context, Camera camera)
    {
        SetStencilFunction(EQUAL, m_StencilValue); // Only render when the stencil equals m_StencilValue
        SetStencilOperation(KEEP); // Keep the value for the HDRP camera render

        // After this, HDRP would render the camera only where the stencil operation is verified
    }

    void OnEndCameraRendering(ScriptableRenderContext context, Camera camera)
    {
        SetStencilOperation(INCREMENT);
        DrawCustomObjects(); // Drawing the custom objects should increment the stencil value

        m_StencilValue++;
    }
}

I also thought of hooking up Custom Passes but the problem is the same, I can't find a way to actually set the Stencil Test Function and Stencil Operation.

Is this possible?