@Carl Love Many thanks. I won't pretend I understand your solution, so if you could spend some time explaining to me what you did, I would appreciate it.

As I need to do the same for thousands of models like model, I have encapsulated your solution in a procedure and apply it to model again. 

buildAllPossibleModels := proc(model::list,M::set)
description "This function returns all models generated from a given model and set of monomials.":
local i,k,m,models:
models:= [
    for k,m in model do
        map(subs, m=~ m+~ (subs(i= k, M) minus {`if`}(m::`+`, op(m), m)), model)[]
    od
]:
return(models):
end proc:

However, this function returns 60 new models instead of 56. What did I do wrong?

Would it be threadsafe?  

@mmcdara Many thanks.   keep[1] returns 1D model and not a 3D model like model. Keep should return 56 models in the format as model (nops(model)=3).

@Carl Love Many thanks.  This new section helped me to understand what is going on.  Many thanks.

@Carl Love It seems that this last version took care of CM_IsStandard.   I wlll do some more test if there is still a problem, I'll let you know.   Thank you.  

@Carl Love Many thanks.  As usual I need help to understand why you have used identical. 

Below it is your code modified to what I need. 

restart:
SaveNames:= (excl::uneval, fname::{symbol, string})->
    subs(
        _V= remove(
            type, {anames}(user), 
            {procedure, identical(eval(excl, 2)[], eval(excl, 1))}
        )[],
        proc() save _V, fname; return end proc
    )()
:
(x,y):=(3,5):
Excl:={anames}(user) minus {anames}(procedure); # To avoid typing the variables - far too many variables in a typical example.
                         Excl := {x, y}

(z,w):=(7,9):

SaveNames(Excl, "/Users/eduardo/tmp/V.txt");
restart:
read "/Users/eduardo/tmp/V.txt";
                             w := 9

                             z := 7

I have noticed that if I define SaveNames after Excl, CM_IsStandard will be saved.  How to avoid that?

Could you also tell me why my proc won't work unless I type Excl?  

@acer Many thanks.  I added style=line to plots:-odeplot in all instances in the worksheet.  It seems to do the trick.  I also use plots:-pointplot3d that shows the same problem.  I thought connect would solve the problem but I had to include style=line. I am not sure if it works in all situations.  I will have to run some tests.  

I will edit my reply to add the commenyts with Array later.

@sursumCorda  Here is part of the code (modified to fit here).

dsnmodel := {diff(x(t), t) = -10*x(t) + 10*y(t), diff(y(t), t) = -z(t)*x(t) + 28*x(t) - y(t), diff(z(t), t) = y(t)*x(t) - (8*z(t))/3, x(0) = 1/10, y(0) = 1/10, z(0) = 1/10};

tfinal:=200:
mf:=500000:
dt:=0.001:


dsol1 := dsolve(dsnmodel, numeric, method = rkf45, output = procedurelist,range=0..tfinal,maxfun=mf):

fig:=Array(1..2):
fig[1]:=plots:-odeplot(dsol1, [x(t), y(t), z(t)],refine=2,caption="Fig. 1 - Lorenz system",captionfont = ["ROMAN", 20]):
fig[2]:=plots:-odeplot(dsol1, [x(t), y(t), z(t)],refine=2,caption="Fig. 2 - Another system",captionfont = ["ROMAN", 20],color = "SteelBlue"):
plots:-display(fig);

@acer 

Yes, it does when I Print directly.   Yes for PDF export as well. When I choose Open in Preview Maple sends the doc to printer. 

Print Preview = Print layout Mode?   No, it does not. 

Where do I add style-line?  In plots:-odeplot?

@emendes Just an update.   I installed Maple 2023 over the weekend and the problem persists.   

@Carl Love That is weird! Maple 2002.2 on Mac M1 started freezing on Monday for no reason. Most of the time I had  to kill the process related to it.  Maple 2022.2 on Linux did not show the same problem though.  

@acer Many many thanks.   Please correct me if i am worng.  These new fancy ways open a door of  new possibilities.  Suppose I want to find the indices of a list that corresponds to elements less than 9.   Would the following command be efficient for long lists?

[for t,v in eval(T) do `if`(v<=9,t,NULL); end do];

@acer Thank you ever so much.   No problem to understand your solution.   The problem is: why I did not think of that?  If you have the time and patience, please post the fancy ways with comments.  

@Kitonum Many thanks. I think I can follow all the steps of your solution but if you think that there is something that stands out, please let me know.  

@Carl Love Many many thanks.   I have checked the help file on anames and there is nothing that explicitly mention procedure there. It would be helpful if Maple included it there.  

@dharr As I said in my first post to this question,  I use Grid, solve, simplify and subs extensively. What I noticed was that if there is at least one cpu running at 100%, there is a chance that the calculations will end eventually. However if no cpu is at 100%, it is a bug for sure.   I constantly run something overnight or even for days.