Besides the obvious answer - MORE (but you knew that just based on your heating bills, didn't you?), how much insulation do you need? There are loads of different standards from Energy Star to PassivHaus to your dad ("about this much" ... holds hands apart).
The whole deal rests on the vagueness of the concept of 'enough' insulation. Without much effort, I also recalled current building code standards, International Energy Code, the oh so vague 'super-insulation'... there are a load of different measures. So which one is 'correct' and how much insulation do you need?
Right off let me say there is no objective standard for insulation levels and none of them are 'correct'. I can't even type the word correct in this context without envisioning fingered 'air quotes'. Insulation level recommendations are based on climate zones, energy models and most importantly, extensive real world observation actual energy use and costs. When smart people have loads of controlled data they can draw some pretty good conclusions but not objectively correct ones.
What we can do is find some reasonable yardsticks and a reliable one is the '10 20 40 60' insulation guidelines by Joe Lstiburek of Building Science (If you haven't been to their site, Building Science is the catnip of energy pros). These guidelines call for an R-value of R-10 sub-slab insulation, R-20 basement walls, R-40 building frame walls and R-60 attic insulation anywhere north of the Mason-Dixon line.
Sub-Slab - XPS foam board is the most commonly used sub-slab insulation. R-10 equals 2 inches of XPS foam. If you have a full basement and the slab is not insulated (very likely), insulation can be laid down and a new slab poured. Granted this is a larger project; you will have to move all your college text books.
The Foundation Wall - The foundation wall should be insulated to an R-20. If you've not blessed with the fortune of having an insulating concrete foam (ICF) foundation, there are a few other options. Insulating the exterior is possible but carries a number of limitations (described in this article on basement insulation). Insulating the interior can be done with 2 inches of XPS or closed cell spray foam then framed with a 2 x 4 studs. Add any standard insulation to the stud wall will help reach R-20.
Building Walls - R-40 ... that's a lot of R's! More importantly, the approaches that can achieve this fix thermal bridging issues. Structural Insulated Panels (SIPs) that are sufficiently thick or standard 2 x 6 framing with 4 inches of exterior polyisocyanurate foam board can achieve R-40 insulation. In retrofit situations, polyisocyanurate is typically added to the exterior.
Note: I'll pause here to mention that the insulation approaches should be taken with a few trainloads of salt. There are MANY different ways to achieve appreciable higher insulation levels in basements, walls and attics.
Attics and Ceilings - R-60? What? Now I've just gone loopy. Before I get into the insulation ... air sealing. The attic flat must be absolutely air sealed for the insulation to work. Once the air barrier is sealed, R-60 can be achieved with 2 layers of 12-inch fiberglass cross batts or 20 inches of blown cellulose (allowing for settling).
If you have a cathedral ceiling, you'll have a steeper haul. These roof usually require 6 inches or more of exterior foam sheathing to reach R-60.
There is no correct guideline for how much insulation you need to install. You can reach a point of diminishing returns. I mean how much energy would you save going from R-60 to say R-100? Very little.
OK, I'll give in...here's a link to the Department of Energy's very cool Insulation by Zip Code lookup tool and a chart on current insulation recommendations by climate zone.