I have the following working for the simple case of a non-multi-container in a container:
template <typename MultiContainer, typename SingleContainer>
void check (const MultiContainer& container, SingleContainer& v) {
    if (std::is_same<MultiContainer, typename SingleContainer::value_type>::value)
        return;
    if (is_container<typename MultiContainer::value_type>::value) {
        std::vector<typename MultiContainer::value_type::value_type> a;  // Using vector for this first draft.
        for (const auto& x : container)
            std::copy (x.begin(), x.end(), std::back_inserter(a));
        if (std::is_same<typename MultiContainer::value_type::value_type, typename SingleContainer::value_type>::value)
            v = a;
//      else check<decltype(a), SingleContainer>(a, v);  // Won't compile
    }
}
template <typename MultiContainer, typename SingleContainer>
SingleContainer extractFromMultiContainer (const MultiContainer& container) {
    SingleContainer v;
    check<MultiContainer, SingleContainer>(container, v);
    return v;
}
int main() {
    using Multi = std::list<std::vector<int>>;
    const Multi multi = { {1,2,3}, {4,5}, {6,7,8,9} };
//  using Multi = std::deque<std::list<std::vector<int>>>;
//  const Multi multi = {  { {1,2,3}, {4,5}, {6,7,8,9} },  { {10,11}, {12,13}, {14,15,16} }  };
    const auto v = extractFromMultiContainer<Multi, std::vector<int>>(multi);
    for (int x : v) std::cout << x << ' ';  // 1 2 3 4 5 6 7 8 9
}
But I cannot get the required recursion line in the 'check' function above working to handle the container-in-container-in-container case (must work no matter how deeply nested actually). I'm using vector as SingleContainer for this first draft (I'll try to generalize that later). Incidentally, I obtained the code of is_container from a previous thread in stackoverflow Determine if a type is an STL container at compile time, so we can just take that part for granted:
template<typename T>
struct has_const_iterator {
private:
    typedef char yes;
    typedef struct { char array[2]; } no;
    template<typename C> static yes test(typename C::const_iterator*);
    template<typename C> static no  test(...);
public:
    static const bool value = sizeof(test<T>(0)) == sizeof(yes);
    typedef T type;
};
template <typename T>
struct has_begin_end {
    template<typename C> static char (&f(typename std::enable_if<
      std::is_same<decltype(static_cast<typename C::const_iterator (C::*)() const>(&C::begin)),
      typename C::const_iterator(C::*)() const>::value, void>::type*))[1];
    template<typename C> static char (&f(...))[2];
template<typename C> static char (&g(typename std::enable_if<
      std::is_same<decltype(static_cast<typename C::const_iterator (C::*)() const>(&C::end)),
      typename C::const_iterator(C::*)() const>::value, void>::type*))[1];
    template<typename C> static char (&g(...))[2];
    static bool const beg_value = sizeof(f<T>(0)) == 1;
    static bool const end_value = sizeof(g<T>(0)) == 1;
};
template<typename T> 
struct is_container : std::integral_constant<bool, has_const_iterator<T>::value && has_begin_end<T>::beg_value && has_begin_end<T>::end_value> {};
 
     
    