My wife is a native Romanian speaker and tells me that this sentence forms what is called a 'cacofonie' (English cacophony: a harsh, discordant mixture of sounds) since 'pisică' ends in the same sound which immediately follows it in 'ca'. 'Ca' in this sentence should thus be replaced with 'precum' - which means the same thing as 'ca': like (in English). So, to be clear, 'Vrei o pisică precum asta?' is the way Romanians would say this.
If two consecutive CV syllables with /k/ bothers them so much, why did they use it in the name for it? Ayyyy
(Just to be clear, I'm not writing this to disagree with you, just to address people concerned with cacophonies).
see the following tables for the forms that go before a noun (and in parentheses the deviation of the forms after OR replacing a noun), e.g. "Acest măr e bun" ("Măr acesta e bun" OR "Acesta e bun.")
official (lat. ecce-istum = look-this)
m acest(+a) acești(+a)
f această(/a) aceste(+a)
popular (lat. istum) ---> omit ecce- = ace-, and restore i- of istum as: m: ă- / f: a-
m ăst(+a) ăști(+a)
f astă(/a) aste(+a)
regional (lat. istum) ---> keep Latin i- at the beginning
m ist(+a) iști(+a)
f iastă(/a) iaste(+a) or ieste(+a)
official (lat. ecce-illum = look-that)
m acel(+a) acei(+a)
f ace(+e)a acele(+a)
popular (lat. illum) ---> omit ecce- = ace-, and restore i- of illum as: m: ă- / f: a-
m ăl(+a) ăi(+a)
f a(+ia) ale(+a)
So far as to the nominative=accusative forms. There will be the same amount of forms for genetive=dative, eventually... ecce homo :-)
Source: https://dexonline.ro/definitie/acest (tab declinări) etc.