  As is well-known, the dimension of the space spanned by the non-degenerate
invariant symmetric bilinear forms (NISes) on any simple finite-dimensional Lie
algebra or Lie superalgebra is equal to at most 1 if the characteristic of the
algebraically closed ground field is not 2.
  We prove that in characteristic 2, the superdimension of the space spanned by
NISes can be equal to 0, or 1, or $0|1$, or $1|1$; it is equal to $1|1$ if and
only if the Lie superalgebra is a queerification (defined in arXiv:1407.1695)
of a simple classically restricted Lie algebra with a NIS (for examples, mainly
in characteristic distinct from 2, see arXiv:1806.05505).
  We give examples of NISes on deformations (with both even and odd parameters)
of several simple finite-dimensional Lie superalgebras in characteristic 2.
  We also recall examples of multiple NISes on simple Lie algebras over
non-closed fields.
