The authors introduce and discuss a family of site decorations which change local lattice features, such as coordination number and planarity, but which may be shown explicitly to preserve the usual percolation exponents even in a continuum limit. The continuum limit is shown to be equivalent to cell percolation where sites are randomly and independently distributed in space, but where connectivity is determined by a cell structure. Conjectured amplitude relationships are verified within lattice families without recourse to scaling arguments.