languages that Have suffixes like Italian and Spanish.

"Gatico" sounds too Colombian, therefore I don't like it, the right form should be Gatito, Perrito, etc.

Where I live we say perrino, gatino, ...

Occitan :

can, gos (chien) – canhòt, gosset (jeune chien, chiot) – canhàs (énorme chien)

gat (chat) – gaton (chaton) – gatonet (tout petit chat) – gatoneton (encore plus petit) – gatàs (gros chat) – gatonàs (vilain petit chat) – gatonetàs (vilain petit chat, plus fort)

femna (femme) – femnòta (petite femme) – femnassa (grosse femme)

filha (fille) – filhòta (petite fille) – filhetassa (petite fille laide ou grosse)

ostal (maison) – ostaleton (petite maison) – ostalàs (grande maison laide)

pichon (petit) – pichonèl (tout petit) – pichoneta (petite affectif) – pichonetàs (petit et mal fait)

<<English, in addition to using -(e)y or -ie (birdie, duckie)/-o (weirdie/weirdo) also has:
-ock (bullock, hillock, buttock)
-ling (duckling, hireling, gosling, underling)
-kin [from Dutch/Low German] (napkin, munchkin)


and [from French, addapted to English words]
-et (midget<midge)
-rel (mongrel, wastrel)
-let (eyelet, piglet) >>


English also has -en
chicken (<cycen 'young bird' < coc/cuc 'fowl/cock')
kitten (< cat)
maiden (<maid)
though also probably no longer productive

No, -en isn't productive at all.

Portuguese has:

-aço, -aça; -ão, -ona; -alhão; -anha; -alha; -eiro; -eira;-arra; -arrão;-az; -ázio, -ágio; -orra.

ricaço; bigodaça; casarão; mulherona; dramalhão; montanha; muralha; maluqueira; mexeriqueiro

and


-acho; -eta, -ete; -ico; -ilho, -ilha; -elho, -elha; -im; -inho, -inha; -ito, -ita; -ola; -ulo; -ela; -eto; --ote; -ucho; -únculo;-zinho

fogacho; cançoneta; ramalhete; burrico; pecadilho; anilha; garotelho; varandim; mocinho; casinha; cãozito; pequenita; criançola; montículo
.

too many for my taste, one or two is fine.