1) You can overload a builtin function or sealed class (like axes), and in the overloaded function define some dynamic properties
2) To add dynamic “methods” which don’t require empty parentheses when called, take @Yair’s implementation and then also define the “GetMethod” parameter of that dynamic property to be the same function handle that you set the property to.

I’m still learning OOP, and am very new to design patterns, but perhaps this is how to implement a decorator pattern in MATLAB, given that sealed classes cannot be subclassed?

function ax = axes(varargin)

   % Create a builtin axes object
   ax = builtin('axes',varargin{:});

   % Add a dynamic method
   p = addprop(ax,'newmethod');
   ax.newmethod = @(x)fun(ax); % Maybe there's a better way to pass the axes to an anonymous function?
   p.GetMethod = @(x)fun(ax);
   p.SetAccess = 'private';

   function out = fun(ax)
      % Do stuff here
   end
end

Now you can call the dynamic “method”, newmethod, without using parentheses, and the object is passed to newmethod when called, just as in a normal class method:

a = axes;
a.newmethod;

Supporting @Yair’s point of view, I also find the sealing of HG classes vexing. Although the dynamicprops approach may suit small programs or ad hoc solutions, it’s not applicable for large projects or general cases. IMHO, a proper inheritance is invaluable in this matter. Perhaps we could write a petition to TMW and ask for the seal to be broken?