There are several mantras that are combinations of the mantras of two deities. Some examples of three popular such deities used in our lineage: Rājagopāla, Sharabheśvara, and Nṛsiṃha.
Rājagopāla:
– Gopālasundarī: Tripurasundarī and Rājagopāla
– Srīvidyārāma: Tripurasundarī and Rāmacandra
– Gopālabālā: Guptagopāla and Bālā ṣaḍakṣarī
– Kāmadhenu: Hādi Saptadaśī and Caturakṣara Gopāla
– Kalpataru: Hādi Pañcadaśī and Caturakṣara Gopāla
– Chintāmaṇi: Hādi ṣoḍaśī and Caturakṣara Gopāla
Sharabha/Nṛsiṃha:
– Astranṛsiṃha: Mantrarāja Nṛsiṃha, Sudarśana and Aṣṭākṣarī
– Sharabhasiṃha: Sharabheśvara and Nṛsiṃha
– Mahāśarabhaśūlinī: Sharabheśvara and Shūlinī Durgā
– Mahāśarabhakālikā: Sharabheśvara and Atharvaṇa Bhadrakālī Pratyaṅgirā
– Mahāśarabheśvara: Sharabheśvara, Shūlinī Durgā and Atharvaṇa Bhadrakālī Pratyaṅgirā
– Aśu Sharabha: Sharabheśvara and Garuḍa Pañcākṣara
– Sharabha Bhairava: Sharabheśvara and Aghora
– Aghora Nṛsiṃha: Mantrarāja Nṛsiṃha and Aghora
– Gāruḍa Nṛsiṃha: Mantrarāja Nṛsiṃha and Garuḍa
– Pāśupata Nṛsiṃha: Aṣṭākṣara NṛSiṃha and Pāśupatāstra
– Nārasiṃhāstra: Bīja Nṛsiṃha, Mantrarāja and Turīyā Gāyatrī
– Stambhana Nṛsiṃha: Bagalāmukhī and Nṛsiṃha
– Chintāmaṇi Nṛsiṃha: Ardhanārīśvara and Nṛsiṃha
– Kśiprasiṃha: Tvaritā and Nṛsiṃha
– Gajamukhasiṃha: Nṛsiṃha, Vakratuṇḍa and Heramba
– Vijaya Nṛsiṃha: Nṛsiṃha and Trailokyavijayā
– Barbarasiṃha: Nṛsiṃha and Vārāhī
There are innumerable such combinations with śrīvidyā as well, mainly using Kādi Pañcadaśī. There are also four such peculiar deities from Kālīkula who are worshiped in the fourteenth āvaraṇa of the Nirvāṇasundarī Krama: Dakṣiṇā-Smaśāna Kālī, Bhadra-Santāna Kālī, Haṃsa-Cintāmaṇi Kālī and Kāmakalā Guhyakālī. It is however interesting that these mantras are not mere combinations of the mantras of two deities (such as Bhadrakālī and Santānakālī).