(Note: I am not an expert on the languages Nepal. The following has been gleaned from teaching Nepalese students, especially recently, and Wikipedia.)
I have mentioned that Nepali is an Indo-European language (here and here), and therefore has some words which are cognate (or might be) with English. Yesterday a Nepalese student said that he and another Nepalese student speak different first languages (alongside standard Nepali as a second language), but don’t understand the other’s language. I caught what one said his language is, made easier by the fact that he uses the ethnic group/language name as his surname. For privacy I won’t tell you which one. I looked at Wikipedia’s list of languages of Nepal and found that that language is actually Sino-Tibetan, and thus more closely related to the languages of China.
Today I asked the other what his first language is, and it is the name of his his ethnic group, but he doesn’t use it as his surname. It is Sino-Tibetan as well, but saying that two Nepalese languages are both Sino-Tibetan says as much about their mutual intelligibility as saying that Romanian and Bulgarian are both Indo-European does (they are from different branches of Indo-European – Romance and Slavic respectively). There is comparatively less information about Sino-Tibetan languages on the internet, and what there is is dominated by Chinese, Tibetan and Burmese, being three national-level languages. (Possibly the two students’ languages are from the same branch (Wikipedia’s article on Sino-Tibetan languages colour-codes them as ‘other’), which might make them as mutually intelligible as Norwegian and Swedish, or Serbian and Croatian, but this seems not to be the case.)
So, three of my current students (an Indian student in another class), speak an ethnic or regional language, their national language (Hindi and Nepali) and their current level of English. And I speak approximately 1.1 languages. Luckily, people want to learn my language, otherwise I’d be out of a job.
Wikipedia’s article on the languages of Nepal states that the 2011 census lists 123 languages spoken in Nepal, but some of those are Indian and others are completely foreign (for example, 8 speakers of Arabic, 16 of Spanish and 34 of French). Slightly fewer than half are Indo-European, but they have larger numbers of speakers each, including the top four, accounting for over 66% of Nepalese between them (adding second language speakers of Nepali totals more than 100%, because many speakers of languages 2-4 also speak Nepalese as a second language (it is a compulsory subject at school, and the medium of instruction in most)). Slightly more than half are Sino-Tibetan, but they have fewer speakers each, under 10,000 in most cases and under 100 in some others. Wikipedia’s article on the demographics of Nepal lists 26 ethnic groups with more than 100,000 members, then combines the rest as ‘more than 100 caste/ethnic groups’, so in effect each caste/ethnic group has its own language.