Can a country face a Malthusian-style constraint from migration rather than births?

If you think migration raises living standards, what mechanism breaks the Malthusian logic (more people → diluted resources) here? In particular, is there any reason to expect per-person productivity to rise with migration, rather than just total output and if so, why?
If housing and infrastructure supply are slow to adjust, wouldn’t population growth simply be capitalised into higher rents and congestion, leaving real income per person roughly unchanged?