Actually as of today there are 2 type of Composition scheme is available .
1. In first scheme you cannot supply services more than 10% of turnover in previous year. hence this scheme is not available to you as nursing home services are cover under supply of Services.
2. As per Notification 2/2019 CT (R) can supply of services or Goods or both, but the turnover not exceeding 50 lac & need to pay tax 6% on turnover. MOST IMPORTANT , cannot do Exempted Supply.
Hence in my view, NO the nursing home cannot opt for composition scheme.