It may not be the worse problem in the world but owning more than 4 rental homes may start to be a problems with lenders. Most lenders these days limit an investor to have 4 non owner occupied homes loans. Some lenders will allow up the FNMA maximium of 10 home loans outstanding. This 5-10 home loan window is restricted to only Rate & Term refinances and no cash outs typically.
There are other sources for financing when you hit this limit - but these are portfolio lenders and the rates and hoops to jump through become more difficult.
Alternative products such as 5+ unit apartment buildings and retail investment commercial real estate are non-restricted options if an additional single family home rental may not be.
It is always a good idea to talk to a reputable lender - especially one who deals with investment properties on a regular basis - before taking on the next investment property purchase.
