Using MemoryRouter inside of BrowserRouter

In my project, I have to navigate from one component to other without changing the url. For this, I used MemoryRouter which worked as expected. But now the same idea should work for different routes i.e /one and /two. For example,

/one --> BrowserRouter (url change visible)
    /
    /first
    /second
    /third
/two --> BrowserRouter (url change visible)
    /
    /first
    /second
    /third

For the new visible routes, i.e /one and /two, the already established working Memoryroutes (i.e /, /first, /second, /third) should work properly with respective data as per provided in /one and /two.

I am struggling to include the MemoryRoutes inside the BrowserRoutes with the following structure code:

    <BrowserRouter>
      <Switch>
        <Route path="/one" render={() => <MemoryComp configFor="Dave"></MemoryComp>}></Route>
        <Route path="/two" render={() => <MemoryComp configFor="Mike"></MemoryComp>}></Route>
      </Switch>
    </BrowserRouter>

and then the MemoryComp holds:

  <MemoryRouter history={customHistory}>
    <Switch>
      <Route path="/" render={(props) => <InitPage configFor={this.props.configFor} history={props.history}></InitPage>}></Route>
      <Route path="/first" component={FirstPage}></Route>
      <Route path="/second" component={SecondPage}></Route>
      <Route path="/third" component={ThirdPage}></Route>
    </Switch>
  </MemoryRouter>

What I am trying to achieve:

• To make the screens work with BrowserRouter --> MemoryRouter configuration.
• To pass data from memory route to another memory route based on the main browser route. (Trying to use history to achieve the same)

Note: This is more likely better to handle the browser routing stuff with server routing instead. Also, this seems can be achieved with any react-stepper plugin. But trying to understand what I am doing wrong here, just for learning purpose.

Here is the whole minimized code, available on Stackblitz (not working):

import React, { Component } from 'react';
import { render } from 'react-dom';
import './style.css';
import { BrowserRouter, MemoryRouter, Route, Switch } from 'react-router-dom';
import { createBrowserHistory } from "history";

const customHistory = createBrowserHistory();

class MemoryComp extends Component{
  render(){
    return(
      <MemoryRouter history={customHistory}>
        <Switch>
          <Route path="/" render={(props) => <InitPage configFor={this.props.configFor} history={props.history}></InitPage>}></Route>
          <Route path="/first" component={FirstPage}></Route>
          <Route path="/second" component={SecondPage}></Route>
          <Route path="/third" component={ThirdPage}></Route>
        </Switch>
      </MemoryRouter>
    );
  }
}

class InitPage extends Component{
  render(){
    return (
      <>
        <ul>
          <li onClick={() => this.navigateTo("/")}>Init</li>
          <li onClick={() => this.navigateTo("/first")}>First</li>
          <li onClick={() => this.navigateTo("/second")}>Second</li>
          <li onClick={() => this.navigateTo("/third")}>Third</li>
        </ul>
        <div>{this.props.configFor}</div>
      </>
    )
  }

  navigateTo(path){
    this.props.history.push(path, {
      data: {
        configFor: this.props.configFor
      }
    })
  }
}

class FirstPage extends Component{
  constructor(props){
    super(props);
    this.data = this.props.history.location.state.data;
  }
  render(){
    return (
      <>
        <ul>
          <li onClick={() => this.navigateTo("/")}>Init</li>
          <li onClick={() => this.navigateTo("/first")}>First</li>
          <li onClick={() => this.navigateTo("/second")}>Second</li>
          <li onClick={() => this.navigateTo("/third")}>Third</li>
        </ul>
        <div>first page</div>
      </>
    )
  }

  navigateTo(path){
    this.props.history.push(path, {
      data: {...this.data, ...{pageName: 'first'}}
    })
  }
}

class SecondPage extends Component{
  constructor(props){
    super(props);
    this.data = this.props.history.location.state.data;
  }
  render(){
    return (
      <>
        <ul>
          <li onClick={() => this.navigateTo("/")}>Init</li>
          <li onClick={() => this.navigateTo("/first")}>First</li>
          <li onClick={() => this.navigateTo("/second")}>Second</li>
          <li onClick={() => this.navigateTo("/third")}>Third</li>
        </ul>
        <div>second page</div>
      </>
    )
  }

  navigateTo(path){
    this.props.history.push(path, {
      data: {...this.data, ...{name: 'deducedValue'}}
    })
  }
}

class ThirdPage extends Component{
  constructor(props){
    super(props);
    this.data = this.props.history.location.state.data;
  }
  render(){
    return (
      <>
        <ul>
          <li onClick={() => this.navigateTo("/")}>Init</li>
          <li onClick={() => this.navigateTo("/first")}>First</li>
          <li onClick={() => this.navigateTo("/second")}>Second</li>
          <li onClick={() => this.navigateTo("/third")}>Third</li>
        </ul>
        <div>third page</div>
      </>
    )
  }

  navigateTo(path){
    this.props.history.push(path, {
      data: this.data
    })
  }
}

class App extends Component {
  constructor() {
    super();
    this.state = {
      name: 'React'
    };
  }

  render() {
    return (
      <div>
        <BrowserRouter>
          <Switch>
            <Route path="/one" render={() => <MemoryComp configFor="Dave"></MemoryComp>}></Route>
            <Route path="/two" render={() => <MemoryComp configFor="Mike"></MemoryComp>}></Route>
          </Switch>
        </BrowserRouter>
      </div>
    );
  }
}

render(<App />, document.getElementById('root'));