  This paper surveys results about token addition and removal (TAR)
reconfiguration for several well-known vertex set parameters including
domination, power domination, standard zero forcing, and PSD zero forcing. We
also expand the range of parameters to which universal $X$-set TAR graph
results apply, for $X$-sets and their TAR graphs introduced in [B. Bjorkman, C.
Bozeman, D. Ferrero, M. Flagg, C. Grood, L. Hogben, B. Jacob, C. Reinhart,
Power domination reconfiguration, arXiv:2201.01798] and [N.H. Bong, J. Carlson,
B. Curtis, R. Haas, L. Hogben, Isomorphisms and properties of TAR
reconfiguration graphs for zero forcing and other $X$-set parameters,
\emph{Graphs Combin.} {39} (2023), Paper No. 86]. Here we examine which of the
$X$-set axioms are needed for which results. The main results apply to skew
zero forcing and vertex covering, and results about TAR reconfiguration graphs
of these parameters are presented. While $X$-sets are defined for parameters
that take the minimum cardinality over the $X$-sets of a graph, and $X$-set
results are restricted to such minimizing parameters, our expansion of the
universal perspective allows these results to be applied to parameters that
take the maximum value among relevant sets, called $Y$-sets. Maximizing
parameters to which the main results apply include independence number, (upper)
irredundance number, and (upper) zero forcing irredundance number, and failed
zero forcing number; TAR reconfiguration results are presented for these
parameters. We also show that the equivalence of connectedness in certain token
jumping reconfiguration graphs and certain TAR reconfiguration graphs for
independent sets established in [M. Kami\'nski, P. Medvedev, M. Milani\v c.
Complexity of independent set reconfiguration problems. {\em J. Theoretical
Computer Science} 439 (2012), 9--15.] extends to $X$-set and $Y$-set
parameters.
