Use custom ticks on FrameTicks on LogLogPlot but preserving the log tick marks

Question

I am wondering if there is a way to use custom ticks on FrameTicks but keep the tick "line marks" for the LogLog plot or LogLinear plot. This is the original plot:

I want to switch the tick into the following, but keep the tick "line marks" for the log axis. Here the tick "line marks" disappear.

The following code is used:

plist = Table[RandomReal[{0, 10000}], 100];
myTicks = Table[{10^i, Superscript[10, i]}, {i, -20, 15}];

(* without ticks *)
ListLogLogPlot[plist, Frame -> True,
 PlotRange -> {All, All}, PlotStyle -> {Thick, Black}, 
 PlotMarkers -> \[EmptyCircle]
 ]

(* with ticks *)
ListLogLogPlot[plist, Frame -> True,
 PlotRange -> {All, All}, PlotStyle -> {Thick, Black}, 
 PlotMarkers -> \[EmptyCircle],
  FrameTicks -> {{myTicks, None},{myTicks, None}} 
 ]

Answer 1

The list of tick marks can be in any order, so all we need to do is append the unlabeled tick marks to the existing list.

labeledTicks = Table[{10^i, Superscript[10, i]}, {i, -20, 15}];

The unlabeled ticks can be generated by multiplying each of the labeled ones by the integers 2 through 9. Strictly speaking, the unlabeled ones have Null as their labels.

unlabeledTicks = Flatten[Table[{k*j, Null}, 
                     {k, 2, 9}, {j, labeledTicks[[All, 1]]}], 1];

Then

myTicks = Join[labeledTicks, unlabeledTicks];

(*with ticks*)
ListLogLogPlot[plist, Frame -> True, 
    PlotRange -> {All, All}, PlotStyle -> {Thick, Black}, 
    PlotMarkers -> \[EmptyCircle], 
    FrameTicks -> {{myTicks, None}, {myTicks, None}}]