Two and three is perfectly fine and the multilevel model can handle imbalance so you can have 2's and 3's in the same model

I have written more extensively about this here

https://www.researchgate.net/post/HLM_MLM_Is_there_a_minimum_number_of_trials_or_conditions_that_can_be_nested_within_individuals

They key is that you will be able to say little about any specific level-2 unit (as you have little information to do so) but you should be able (provided you have plenty of level 2 units) to estimate the between and within variance eg the between household and within household decomposition.

You may want to read this (unfinished) paper to understand about imbalance and precision-weighted estimation and the benefits that multilevel modelling brings

https://www.researchgate.net/publication/252146040_Do_multilevel_models_ever_give_different_results

and also this rather older paper which demonstrates the precision-weighted nature of the estimates

https://www.researchgate.net/publication/225303298_Contextual_Models_of_Urban_House_Prices_A_Comparison_of_Fixed-and_Random-Coefficient_Models_Developed_by_Expansion

and this recently submitted one 

https://www.researchgate.net/publication/299604336_Fixed_and_Random_effects_making_an_informed_choice

Article Contextual Models of Urban House Prices: A Comparison of Fix...

Article Do multilevel models ever give different results?.

Article Fixed and Random effects models: making an informed choice