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It is not clear how many coefficients should be used.
We may need more, the same, or less than the number
of pattern variables.
Coefficients in a multivariate series typically became larger
hence we would like to use the smallest first few coefficients.
This suggests an iterative approach.
Compute the first non-zero coefficient of the series, and solve
it for any of the parameters.
Plug in the result in the original pattern and expand again.
This guarantees to use the right number of coefficients.
On the other hand it forces several invocations of the solver,
and sometimes it is better to give the whole system to the solver
and let it do the best possible job.