I think you can save each plot in a plot variable and then displaying them in the same graphic:

with(DEtools):with(plots):
>
> k:= 0.1:
>
> q:=0.5:
>
> M:= 3:
>
> MM:= k*M/(1-q)*q^(q/(q-1)):
>
>  
>
> EQ1:= diff(N1(t), t) = k*M/(1-q)*(N1(t)/M)^(1-q);
>
>  
>
> EQ2:= diff(N2(t), t) = k*M/(q-1)*(1 - (N2(t)/M)^q - (1 - N2(t)/M)^q );
>
>  
>
> EQ3:= diff(N3(t), t) = MM*(N3(t)/M)^q *(1- (N3(t)/M)^(1-q));
>
>  
>
> P1:=DEplot(EQ1, N1(t), t = 0 .. 40, [N1(0) = .99],color=blue,linecolor=black):
> P2:=DEplot(EQ2, N2(t), t = 0 .. 40, [N2(0) = 0.1e-1],color=green,linecolor=violet):
> P3:=DEplot(EQ3, N3(t), t = 0 .. 40, [N3(0) = .5]):
>display(P1,P2,P3,view=[0..40,0..3]);

the output is not very pretty, but I hope it solves your question.

Regards.

Gabriel Torrealba.