To solve this optimization problem using Gurobi, we need to translate the given objective function and constraints into a mathematical model that can be expressed in code. The goal is to maximize the value of 3 times the number of milligrams of vitamin K plus 6 times the number of milligrams of vitamin D.

The variables are:
- `x0`: milligrams of vitamin K
- `x1`: milligrams of vitamin D

Given constraints and objective function can be directly translated into Gurobi code. 

```python
from gurobipy import *

# Create a new model
m = Model("Vitamin_Optimization")

# Define the variables
x0 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_K")
x1 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_D")

# Objective function: Maximize 3*x0 + 6*x1
m.setObjective(3*x0 + 6*x1, GRB.MAXIMIZE)

# Constraints
# Kidney support index constraints
m.addConstr(7*x0 + 11*x1 >= 17, name="kidney_support_index_min")
m.addConstr(7*x0 + 11*x1 <= 54, name="kidney_support_index_max")

# Energy stability index constraints
m.addConstr(x0 + 9*x1 >= 27, name="energy_stability_index_min")
m.addConstr(x0 + 9*x1 <= 83, name="energy_stability_index_max")

# Immune support index constraints
m.addConstr(5*x0 + 5*x1 >= 22, name="immune_support_index_min")
m.addConstr(5*x0 + 5*x1 <= 28, name="immune_support_index_max")

# Additional constraint: -10*x0 + 3*x1 >= 0
m.addConstr(-10*x0 + 3*x1 >= 0, name="additional_constraint")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of Vitamin K: {x0.x}")
    print(f"Milligrams of Vitamin D: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")

```
```python
```