A) what’s a top school?
B) what are her stats. Last year posts made it seem like she was a bit under water rigor wise. So is a perceived top school even possible?
Depending on stats, she can be out well under $200K. Again, in engineering - look at my son, turned down Purdue for Alabama. He’s far from the only. Certain schools buy kids in. I spent maybe $70K over four years - but it’s stat dependent. Who does he work with? Michigan, Case Western, Washington, UC Something but also W MIchigan, Akron, Buffalo. They all come in together. That’s how engineering is - ABET is often the baseline organizations use. They literally write it in job descriptions. One of his offers was in Mass. They seemed to have a lot of RPIs per people in the program (he only applied to Rotational programs and that company was a major defense contractor).
What is your state? That can bring discounts.
Per College Transitions, some of your low costs engineering top PHD feeders per capita -
Olin - it’s heavily scholarshiped
RPI - lots of merit
Rose Hulman - lots of merit - #1 ranked amongst schools not offering a PHD
New Mexico Tech - low cost (#10 on the per capita feeder list)
#11 is Clarkson - my friend’s kid goes for under $40K
#12 is Missouri Science and Tech - low cost + merit
Also low cost on the top PhD list - Michigan Tech, Florida Tech, etc.
I do think you’re presumptuous on a few things:
- The Italian degree appears to be 3 years. Does it have enough credits/rigor
- That she’ll finish in engineering - half don’t. It’s a tough major - my stud kid had to withdraw a math class his first semester. Yeah, he retook with an A - but it’s hard. Many go to other majors. His friends at other schools had similar experiences.
- That’s she’ll pursue a Masters. Some do - but not everyone - and some do it, for example, at my son’s school - because they were NMFs and had 5 years paid for in scholarship so not to waste it. Others, do a different Masters like business - but after they’ve worked a few years.
- You also mentioned a PhD - and I think she’s 17/18 - and I think it’s great if it happens - but you are planning a life that is unlikely to go int he linear pattern you think.
I’m not saying she shouldn’t pursue Italy. If that’s what she really wants. I do think you are planning a little too much long term.
And I do think if you are budget conscious, that’s not a problem here. I also think your over focus on rank, especially in engineering, is not necessary.
We don’t know anything about her stat wise - maybe you should do a match me - since you are budget constrained.
And then the question becomes - are you full pay or do you qualify for need - because if you qualify for need, there are schools that might bring your cost down anyway.
If you read any of the feeds, you will see a lot of schools today are buying kids. It’s a competitive world and they’d rather pay for kids to come in vs. having empty seats.
If it’s truly Italy or Europe she wants - I wish her well. Would a Canadian school - not sure the costs - but in Quebec but a reasonable sub ? I know McGill speaks English - I don’t know the costs and nuances of engineering but it’s popular on the CC. They say Montreal is European
I was there last summer - ehhhhh. Quebec City moreso. Or might another continent like Australia work - again, I don’t know the nuances of engineering. Or England or Ireland - all speaking English 
Good luck.