In the past, I have tried to balance the concepts of raising too little and alternatively of raising 'too much'. The concept of too much, in my case, has been based on the expectation that each time we seek funding, our company has increased in value and so we can sell shares for a higher per share price. In that context, it is better to sell eg 100,000 shares now for $5 each and another 100,000 shares later for $10 each. So I preferred the concept of getting funding in small drip-fed amounts.
This seems intuitively sensible. But, conventional wisdom says you should have sufficient funding for 6 - 12 months. And it is easiest to raise additional money when you're not visibly desperate for funds. You probably know the saying "The easiest way to raise money is to show you don't need it". And, similarly, "The best time to raise money is when you already have lots".
Having suffered the consequences of not having a 6 - 12 month 'runway' of funding, I'd now much prefer to sell 'too many' shares at 'too low' a price. The value in return - security for extended continuing operations - is worth any amount of premium you might feel you're paying for it.
Raising 'only' 10% - 20% extra is very modest. Depending on the product you are developing, many investors will tend to adjust your projections, increasing your costs, reducing your revenues, and lengthening the lead-times to get your product to market. This would have them seeing a need for very much more than an extra 10% - 20%. It is not unheard of for potential investors to adjust these items by a factor of two or more - obviously, the further along the road to success, the less these factors need to be adjusted.
No-one will accuse you of being greedy. You are being prudent and protecting your future - and therefore, their future too!
My recommendation? Don't just add an extra 10% - 20% cushion. Make sure you have your 6 - 12 months of funding, and then add an extra 50%. Tell your investors that by over-funding, you are reducing the biggest risk all new companies have - the risk of running out of capital.