The Italian embassy won't care about your trips to non-Schengen countries; to them, you're merely visiting Italy for tourism. And given that your itinerary doesn't involve exiting and re-entering the Schengen Area, you're probably not going to get a double-entry visa, let alone a multiple-entry one. There is no "hack" to make this happen
As stated by Timatic, the database used by airlines:
Romania:
Visa required, except for Passengers with a double or multiple
entry C visa issued by a Schengen Member State valid for the period of intended stay
Serbia:
Visa required, except for Passengers with a multiple entry or
an unused one-entry visa issued by Switzerland, USA or an EEA
Member State for a maximum stay of 90 days
and
Visa required, except for Passengers with a residence permit,
valid for the period of stay, issued by United Kingdom for a
maximum stay of 90 days
Croatia:
Visa required, except for Passengers with a double or multiple
entry C visa issued by a Schengen Member State valid for all Schengen Member States and valid for the period
of intended stay
So unless you do get at least a double-entry Schengen visa valid on the Dates you visit Croatia and Romania, you will need a Croatian and Romanian visa as well, but not a Serbian visa.
Note that for Romania and Croatia, the Schengen visa must be valid when entering these countries, but for Serbia it doesn't matter, because you can enter either on the basis of a valid (single or multiple) Schengen visa or a valid UK residence Permit. You have the latter, so no matter what, you will not Need a Serbian visa