code review - How to deal with the condition that a function own many options?

Assming that I have a function myFunc which has some options.

Options[myFunc]={ firstOpt->1, secondOpt->"A", thirdOpt->True };

where, I set the values of firstOpt to 1 or 2,and set the value secondOpt to "A" or "B".

myFunc[arg1_,arg2_,OptionsPattern[]]:=
 Module[{method},
  method= OptionValue/@{firstOpt,secondOpt,thirdOpt};
  Switch[
   method,
   {1,"A",True},subFunc1[...],
   {2,"A",True},subFunc2[...],

   {1,"B",True},subFunc3[...],
   {2,"B",True},subFunc4[...],
   {1,"A",False},subFunc4[...],
   {2,"A",False},subFunc5[...],
   {1,"B",False},subFunc6[...],
   {2,"B",False},subFunc7[...],
  ]
 ]

Obviously, this is a fussy and awkward solution.So I would like to know how to deal with condition when myFunc has many options.

Or is it possible to know Mathematica how to deal with many options? For instance,

 Length@Options@ArrayPlot
 (*48*)

---

An example(Implementation of Runge-Kutta Algorithm)

 (*MiddlePoint formula*)
 middlePointOrderTwo[{xn_, yn_}, step_, func_] :=
  Module[{K1, K2},
   K1 = func[xn, yn];

   K2 = func[xn + 1/2 step, yn + 1/2 step K1];
   {xn + step, yn + step K2}
 ]
 (*Henu formula of order 2*)
 henuOrderTwo[{xn_, yn_}, step_, func_] :=
  Module[{K1, K2},
   K1 = func[xn, yn];
   K2 = func[xn + 2/3 step, yn + 2/3 step K1];
   {xn + step, yn + 1/4 step (K1 + 3 K2)}
 ]

 (*Henu formula of order 2*)
 henuOrderThree[{xn_, yn_}, step_, func_] :=
  Module[{K1, K2, K3},
   K1 = func[xn, yn];
   K2 = func[xn + 1/3 step, yn + 1/3 step K1];
   K3 = func[xn + 2/3 step, yn + 2/3 step K2];
  {xn + step, yn + 1/4 step (K1 + 3 K3)}
 ]
 (*Kutta formula of order 3*)
 kuttaOrderThree[{xn_, yn_}, step_, func_] :=

  Module[{K1, K2, K3},
   K1 = func[xn, yn];
   K2 = func[xn + 1/2 step, yn + 1/2 step K1];
   K3 = func[xn + step, yn - step K1 + 2 step K2];
   {xn + step, yn + 1/6 step (K1 + 4 K2 + K3)}
 ]
 (*Runge-Kutta formula of order 4*)    
 rungeKuttaOrderFour[{xn_, yn_}, step_, func_] :=
  Module[{K1, K2, K3, K4},
   K1 = func[xn, yn];

   K2 = func[xn + 1/2 step, yn + 1/2 step K1];
   K3 = func[xn + 1/2 step, yn + 1/2 step K2];
   K4 = func[xn + step, yn + step K3];
   {xn + step, yn + 1/6 step (K1 + 2 K2 + 2 K3 + K4)}
  ]

---

  rungeKuttaFormula[{a_, b_}, ya_, step_, func_, OptionsPattern[]] :=
   Module[{OrderMethod, num},
    OrderMethod = OptionValue[SolvingOrderMethod];

    num = IntegerPart[(b - a)/step];
    Switch[
     OrderMethod,
     {2, "Henu"},
     NestList[
      henuOrderTwo[#, step, func] &, {a, ya}, num],
     {2, "MiddlePoint"},
     NestList[
      middlePointOrderTwo[#, step, func] &, {a, ya}, num],
     {3, "Henu"},

     NestList[
      henuOrderThree[#, step, func] &, {a, ya}, num],
     {3, "Kutta"},
     NestList[
      kuttaOrderThree[#, step, func] &, {a, ya}, num],
     {4, "RungeKutta"},
     NestList[
      rungeKuttaOrderFour[#, step, func] &, {a, ya}, num]]
   ]