The purpose of a for-profit corporation is essentially to invest money on behalf of its shareholders, and turn a profit that it can distribute in the form of dividends. More money to invest can = more return, if the company is managed well.
So let's say you're a hotel company: you can buy a hotel for $10M, and you need $1M on hand for each hotel for working capital [to pay salary costs and supplies, etc.], and every year you make let's say $30M in revenue from room bookings, less $25M in expenses from all costs, leaving you with $5M in net income every year.
In your first year, you would need to raise $11M of initial capital to buy your first hotel and get it running. In your 2nd year, you would have $5M in the bank - let's assume you pay $1M back to your shareholders as dividends, so now you have $4M in the bank.
If you want to buy another hotel to double your income, you have two choices: you could wait 3 years to accumulate $12M [because inflation means that the next time you buy a hotel it might be more expensive], or you could raise another $11M through a new share offering. Your old shareholders will get a smaller piece of a bigger pie - actually, they will now get only half of a pie that is twice as big - so they don't care that you do this.
In fact, your old shareholders might feel that you will get more efficient as a hotel over time, so they would prefer that you raise the capital now, and increase the power of your brand sooner, to capitalize [pun] on your current success in the market. Maybe you raise $100M, and you buy 10 hotels [maybe it costs you a little less overall to buy so many at once, etc]. So now your old shareholders would have (11 original shares /111 total shares= ) 9.9% of a pie that is 11x bigger.
But the opposite can also be true. Sometimes, a company has no new valuable projects to invest in, so additional capital would be a waste. For example, what if your hotel brand is an Atlantis-themed resort, and only works on a beachside rocky location in the Mediterranean? Maybe there are only 3 possible spots that you think the theme would work. So getting an extra $100M would still only allow you to invest $~30M of it in new projects. In that case, most shareholders would prefer that you not dilute their shareholdings, and thus you should limit your 2nd share offering to only $30M instead of $100M. There is a risk that if a company grows too large, too quickly, it will lose sight of what made them special in the first place.
This is also (one reason) why some companies pay a lot of dividends, and some companies pay very little in dividends. If you are a junior mining company, for example, you probably need as much cash as possible to build large projects. But if you are a medium-sized mining company, you might decide that you will continue to just operate the mines that you already own, and if you aren't building any new projects, you will pay out almost all of your net income as dividends every year. It then becomes the choice of the shareholders of your company to choose which other mining companies to invest in.
Remember that a well-run company operates in the interest of its shareholders - so if the shareholders would rather have more cash than have their company grow larger, the company wants the same thing. If the company acts in a way not benefiting the shareholders, they can vote in a new board of directors that will better meet their interests.
So yes, a company can continually increase its capital by offering more and more shares, and that may or may not be in the best interest of its shareholders.