How can I render multiple components for a single route?

import React from 'react'
import { BrowserRouter, Route, Link } from 'react-router-dom'

const Links = () => (
  <nav>
    <Link to='/home'>Home</Link>
    <Link to='/about'>About</Link>
  </nav>
)

const Header = ({ match }) => (
  <div className='header'>
    <Route path='/:page' render={({ match }) => (
      <h1>{match.params.page} header</h1>
    )} />
  </div>
)

const Content = ({ match }) => (
  <div className='content'>
    <Route path='/:page' render={({ match }) => (
      <p>{match.params.page} content</p>
    )} />
  </div>
)

const App = () => (
  <BrowserRouter>
    <div>
      <Links />
      <Header />
      <Content />
    </div>
  </BrowserRouter>
)

export default App