Sorting multiple vectors in single sort call C++

This answer demonstrates how to efficiently obtain an indices vector using std::sort on a vector of values using the nice new-ish C++11 functionality (there's also a variety of duplicates of that question as well). It also hints that you can obtain the double output of both the sorted vector and the sorted indices by "using an extra vector." However, the only way I can achieve this is by calling std:sort a second time. I'm working with arrays with lengths of tens, maybe hundreds, of thousands of elements trying to focus on efficiency. Is it possible to obtain both the sorted vector and the indices of the sort from a single call to std::sort?

More generally, my question is: can one sort multiple vectors with a single sort call? The assumption is the sorting order is based on only one of the supplied vectors.

What I've come up with in the meantime is this (a slight modification to the code in the linked answer), but as you can see, it requires a call to std::sort for each vector being sorted, even though they are all to be ordered according to the sorting of a single vector:

#include <numeric>
#include <algorithm>

using std;

void sort_vectors(vector<size_t> idx, vector<double> &v) {

  // sort indexes based on comparing values in v
  sort(idx.begin(), idx.end(),
       [&v](size_t i1, size_t i2) {return v[i1] < v[i2];});

  // Sort the actual vector
  sort(v.begin(), v.end());

  return idx;
}