I am somewhat surprised by my GO enrichment analysis resuts. Is it possible that using gene sets with lower p-value threshold for differential gene expression, gives me more GO terms than using higher p-value threshold? I would expect that as I make the criterion for differential gene expression more stringent, the number of enriched/underepresented terms would go down and certainly no new terms pop up.

Yes, I have got it now... thanks Miguel and the rest of contributors!