In 2001, Congress recognized that an employer’s contribution to a retirement plan for a household employee is non-deductible if the contribution is not made for a trade or business.
See Internal Revenue Code of 1986 (26 U.S.C.) § 4972(c)(6)(B).
https://www.govinfo.gov/content/pkg/USCODE-2017-title26/html/USCODE-2017-title26-subtitleD-chap43-sec4972.htm
IRC § 414(c) refers to “employees of trades or businesses (whether or not incorporated) which are under common control[.]”
If the household employees do no work for a trade or business, there might be no second business to be treated as under common control with the LLC business.