"We want to spend more time in this country."
Translation:Haluamme viettää enemmän aikaa tässä maassa.
You can actually say "lisää aikaa".
"Tarvitsen lisää aikaa." - I need more time (I have time, but I need more in addition to the time I already have)
"Aion ladata lisää aikaa bussikorttiini" - I intend to/I'm going to load more time into my buss pass (in addition to the time I already have in the pass).
With "Haluamme viettää enemmän/lisää aikaa tässä maassa", it's basically the same sentence whichever word you use, but there IS a slight difference as "enemmän" is the comparative form of "paljon" (a lot, much), while lisää is "more" in the sense if "in addition to x".
"Haluan enemmän kahvia" - I want more coffee (a bigger amount)
"Haluan lisää kahvia" - I want more coffee (I already emptied my cup)
It has to agree, are aren’t just in the country, you are in this country. The ending is not like a pronoun that gets attached to one word, it is a case which here indicates something being inside, and the words attached to the noun have to coordinate with the noun and be in that same case.