Spontaneous or conversational multilingual speech presents many challenges for state-of-the-art automatic speech recognition (ASR) systems. In this work, we present a new technique AMPS that augments a multilingual multimodal ASR system with paraphrase-based supervision for improved conversational ASR in multiple languages, including Hindi, Marathi, Malayalam, Kannada, and Nyanja. We use paraphrases of the reference transcriptions as additional supervision while training the multimodal ASR model and selectively invoke this paraphrase objective for utterances with poor ASR performance. Using AMPS with a state-of-the-art multimodal model SeamlessM4T, we obtain significant relative reductions in word error rates (WERs) of up to 5%. We present detailed analyses of our system using both objective and human evaluation metrics.