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We introduce a method that produces a bijection between the posets ${\rmsilt-}{A}$ and ${\rm silt-}{B}$ formed by the isomorphism classes of basicsilting complexes over finite-dimensional $k$-algebras $A$ and $B$, by lifting$A$ and $B$ to two $k[[X]]$-orders which are isomorphic as rings. We apply thisto a class of algebras generalising Brauer graph and weighted surface algebras,showing that their silting posets are multiplicity-independent in most cases.Under stronger hypotheses we also prove the existence of largemultiplicity-independent subgroups in their derived Picard groups as well asmultiplicity-invariance of $\rm TrPicent$. As an application to the modularrepresentation theory of finite groups we show that if $B$ and $C$ are blockswith $|{\rm IBr}(B)|=|{\rm IBr}(C)|$ whose defect groups are either bothcyclic, both dihedral or both quaternion, then the posets ${\rm tilt-}{B}$ and${\rm tilt-}{C}$ are isomorphic (except, possibly, in the quaternion case with$|{\rm IBr}(B)|=2$) and ${\rm TrPicent}(B)\cong{\rm TrPicent}(C)$ (except,possibly, in the quaternion and dihedral cases with $|{\rm IBr}(B)|=2$).

Bijections of silting complexes and derived Picard groups