In short, your scenario could work in theory, but is not realistic...
Generally speaking, you can borrow up to some percentage of the value of the property, usually 80-90% though it can vary based on many factors. So if your property currently has a value of $100k, you could theoretically borrow a total of $80-90k against it. So how much you can get at any given time depends on the current value as compared to how much you owe. A simple way to ballpark it would be to use this formula: (CurrentValue * PercentageAllowed) - CurrentMortgageBalance = EquityAvailable.
If your available equity allowed you to borrow what you wanted, and you then applied it to additions/renovations, your base property value would (hopefully) increase. However as other people mentioned, you very rarely get a value increase that is near what you put into the improvements, and it is not uncommon for improvements to have no significant impact on the overall value. Just because you like something about your improvements doesn't mean the market will agree.
Just for the sake of argument though, lets say you find the magic combination of improvements that increases the property value in line with their cost. If such a feat were accomplished, your $40k improvement on a $100k property would mean it is now worth $140k. Let us further stipulate that your $40k loan to fund the improvements put you at a 90% loan to value ratio. So prior to starting the improvements you owed $90k on a $100k property. After completing the work you would owe $90k on what is now a $140k property, putting you at a loan to value ratio of ~64%. Meaning you theoretically have 26% equity available to borrow against to get back to the 90% level, or roughly $36k. Note that this is 10% less than the increase in the property value. Meaning that you are in the realm of diminishing returns and each iteration through this process would net you less working capital.
The real picture is actually a fair amount worse than outlined in the above ideal scenario as we have yet to account for any of the costs involved in obtaining the financing or the decreases in your credit score which would likely accompany such a pattern. Each time you go back to the bank asking for more money, they are going to charge you for new appraisals and all of the other fees that come out at closing. Also each time you ask them for more money they are going to rerun your credit, and see the additional inquires and associated debt stacking up, which in turn drops your score, which prompts the banks to offer higher interest rates and/or charge higher fees...
Also, when a bank loans against a property that is already securing another debt, they are generally putting themselves at the back of the line in terms of their claim on the property in case of default. In my experience it is very rare to find a lender that is willing to put themselves third in line, much less any farther back. Generally if you were to ask for such a loan, the bank would insist that the prior commitments be paid off before they would lend to you. Meaning the bank that you ask for the $36k noted above would likely respond by saying they will loan you $70k provided that $40k of it goes directly to paying off the previous equity line.