Solution

neuron_classes.cpp

// This is just a pseudo-code.

// 
// File: common_header.hpp
//
void current(state_type &variables, state_type &dxdt, const double t, int index, vector<string> var_param_names_from_isf) {
  // this fucntion has common code
  // just that the name for variable is acquired from
  // var_param_names_from_isf vector by accessing its index
  // e.g. index x - var_param_names_from_isf[x]
}

//
// File: sub_class_1_for_neuron.cpp
//
#include "common_header.hpp"                  // includes the common header file

class SubClass1 {
  void current((state_type &variables, state_type &dxdt, const double t, int index) {
    // fabricate the new vector<string> with this class' 
    // variable and parameter requirements
    std::vector<string> var_params_i_need = {
                                              "parameter1", 
                                              "variable1",
                                              "variable2",
                                              ...  
                                            };
  
    
    // Now call our custom current function from common_header.hpp
    // with the new parameter to the current() at the end
    // of the function arguments
    current(variables, dxdt, t, index, var_params_i_need);
  }
};

// Similarly there can be SubClass2 with same strategy and common current()
// call with its own variable and parameter names

// Comment on this gist if you have questions

Great. This looks like the thing I need. Will get back to you after I try to put this to work.