It would help to have a specific example so readers will know what sorts of equations are being considered. Offhand all I can suggest is to add tag variables and equations to recover the needed partial derivatives. E.g. add equation df1dx3==D[f1,x3] and add df1dx3 to the variable list

I think this isn't possible, but I may be wrong.

Example see here:

 functions = {x^2 + y^2 - 4, E^x + y - 1};
 ResourceFunction["JacobianMatrix", ResourceSystemBase -> 
 "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][functions, {x,y}]//MatrixForm

or:

vars = {x, y};
functions = {x^2 + y^2 - 4, E^x + y - 1};
jacobianUsingOuter = Outer[D, functions, vars];
MatrixForm[jacobianUsingOuter]

Regards M.I.