Discrimination or identification task performance level is a joint function of many factors, including signal contrast, external noise contrast, template overlap (similarity of target stimuli), as well as the state of the observer. The many observer models, including the Linear Amplifier model, the Perceptual Template model (PTM), and the Eckstein-Ahumada-Watson model, were constructed for cases where any single stimulus plausibly activates only one perceptual template (e.g., Gabors of orientation ±45°). In this research, we developed and evaluated an extended PTM to handle cases in which close to-be-discriminated stimuli activate overlapping perceptual templates (e.g., Gabors of ±3°). Threshold versus external noise contrast (TvC) functions were measured in an orientation identification task at fovea for four orientation differences (±3°,±6°,±15°, and ±45° from the vertical) across a range of external noises using the newly developed qTvC procedure (Lesmes, Jeon, Lu & Dosher, 2004) for three observers. The qTvC procedure was used to obtain TvC functions at multiple performance levels with about 500 trials per orientation separation. The extended PTM provided excellent fits to the data in all conditions with changes of a single parameter that characterized the overlap between perceptual templates in different stimulus conditions. In other words, the gain of the perceptual template, the internal noises, and the non-linear transducer remain the same across different orientation conditions. The extended PTM provides a general functional description of identification task performance in different signal contrast, external noise contrast, as well template overlap conditions. It also supports the estimation of feature thresholds.