Market research indicates that fingerprints are still the most popular biometric modality for personal authentication. Even with the onset of new modalities (e.g. vein matching), many applications within different domains (e-ID, banking, border control...) and geographies rely on fingerprints obtained from the distal phalanges (a.k.a. sections, digits) of the human hand structure. Motivated by the problem of poor quality distal fingerprint images affecting a non-trivial portion of the population (which decreases associated authentication accuracy), we designed and tested a multifinger, multiphalanx fusion scheme, that combines minutiae matching scores originating from non-distal (ie. middle and proximal) phalanges based on (i) simple sum fusion, (ii) NFIQ image-quality-based fusion, and (iii) phalanx-type-based fusion. Utilizing a medium-size (50 individuals, 400 unique fingers, 1600 distinct images) database collected in our laboratory with a commercial optical fingerprint sensor, and a commercial minutiae extractor & matcher (without any modification), allowed us to simulate a real-world fingerprint authentication setting. Detailed analyses including ROC curves with statistical confidence intervals show that the proposed system can be a viable alternative for cases where (i) distal phalanx images are not usable (e.g. due to missing digits, or low quality finger surface due to manual labor), and (ii) switching to a new biometric modality (e.g. iris) is not possible due to economical or infrastructure limits. Further, we show that when distal phalanx images are in fact usable, combining them with images from other phalanges increases accuracy as well.