Compressed full-text indexes enable efficient sequence classification against a pangenome or tree-of-life index. Past work on compressed index classification used matching statistics or pseudo-matching lengths to capture the fine-grained co-linearity of exact matches. But these fail to capture coarse-grained information about whether seeds appear co-linearly in the reference. We present a novel approach that additionally obtains coarse-grained co-linearity (“chain”) statistics. We do this without using a chaining algorithm, which would require superlinear time in the number of matches. We start with a collection of strings, avoiding the multiple-alignment step required by graph approaches. We rapidly compute multi-maximal unique matches (multi-MUMs) and identify BWT sub-runs that correspond to these multi-MUMs. From these, we select those that can be “tunneled”, and mark these with the corresponding multi-MUM identifiers. This yields an \(O(r + n/d)\) -space index for a collection of d sequences having a length-n BWT consisting of r maximal equal-character runs. Using the index, we simultaneously compute fine-grained matching statistics and coarse-grained chain statistics in linear time with respect to query length. We found that this substantially improves classification accuracy compared to past compressed-indexing approaches and reaches the same level of accuracy as less efficient alignment-based methods.