This paper considers malleable digital signatures, for situations where data is modified after it is signed. They can be used in applications where either the data can be modified (collaborative work), or the data must be modified (redactable and content extraction signatures) or we need to know which parts of the data have been modified (data forensics). A \new{classical} digital signature is valid for a message only if the signature is authentic and not even one bit of the message has been modified. We propose a general framework of modification tolerant signature schemes (MTSS), which can provide either location only or both location and correction, for modifications in a signed message divided into $n$ blocks. This general scheme uses a set of allowed modifications that must be specified. We present an instantiation of MTSS with a tolerance level of $d$, indicating modifications can appear in any set of up to $d$ message blocks. This tolerance level $d$ is needed in practice for parametrizing and controlling the growth of the signature size with respect to the number $n$ of blocks; using combinatorial group testing (CGT) the signature has size $O(d^2 \log n)$ which is close to the \new{best known} lower bound \new{of $Ω(\frac{d^2}{\log d} (\log n))$}. There has been work in this very same direction using CGT by Goodrich et al. (ACNS 2005) and Idalino et al. (IPL 2015). Our work differs from theirs in that in one scheme we extend these ideas to include corrections of modification with provable security, and in another variation of the scheme we go in the opposite direction and guarantee privacy for redactable signatures, in this case preventing any leakage of redacted information.