Human emotions are complex and cannot occur in singularity. They exist in blends and mixes of more than one emotion. Traditionally, the datasets and computational models were built up either for multi-class, multi-label classification, or simple linear regression for emotion prediction. However, we found a scarcity of computational resources that can aid in detecting the presence of more than one emotion and their strength in text. Therefore, a computational approach needs to be devised for quantifying multiple emotions simultaneously. For devising such an approach, we utilize available textual resources, Tweet Emotion Intensity (EmoInt) and NRC Affect Intensity Lexicon (AIL), for training individual Bidirectional Encoder Representation from Transformer (BERT) regressors for predicting intensities of target emotions, namely, anger, fear, joy, and sadness. All the regressors achieved a Pearson Correlation Coefficient r above 0.7, indicating high correlation. Using these regressors, we annotate a multi-label dataset GoEmotions to generate a Multi-Target GoEmotions (MTGoEmotions) dataset. With MTGoEmotions, we fine-tune a BERT model to perform multi-output regression and output a vector of target emotions intensities. The multi-output regressor performed with a low mean square error MSE of 0.014 and an r of 0.88, indicating very high correlation. Using the intensity vector, we also quantify secondary emotions: pride, guilt, envy, and despair.