George White's answer is very accurate. I will add few things to it.
You can amend your specification and claims upon entering the European phase so that the page fee is reduced, but as pointed out by George White you should be careful with your amendments, Art. 123(2) EPC kills many applications and patents. You can also file divisionals with amended description so that the page fee is not so expensive.
One option you have is enter into the European phase with the complete text and claim the most important inventions right away (there is also the claim fee for claims in excess of 15, so be careful). The EPO will search the first invention and invite you to pay search fees for each further invention claimed. You can pay for the searches you want (but do not claim them if you are not willing to pay for the search at this point in time) so that you get a written opinion for each searched invention and then decide which one to examine in that application and whether any one of the others is to be moved to examined in divisionals (right away or later on). In this way you know before filing some divisionals what is the EPO's preliminary opinion on the patentability of said inventions, maybe you will decide not to file those divisionals if the prior art is very strong. If you were to file any one of those divisionals, you have to pay the search fee again, but it will be reimbursed after some months because you already paid for the search, otherwise the fee will not be reimbursed.
Like in the US, divisionals can be filed as long as one prior application is pending.
If your description is structured such that you described the different inventions in the form of different aspects of the invention, then removing the part related to inventions not claimed should be more or less straightforward.
You may want to read the last chapter of EPO's Euro-PCT Guide that explains the European regional phase in a very understandable manner. It includes references to the applicable articles, rules and guidelines for examination (a very thorough explanation of all aspects related to European patent prosecution).
Lastly, bear in mind that if you are not a natural or legal person resident in a Contracting State of the European Patent Convention, you will have to be represented by a European patent attorney for EPO's proceedings.
P.S. The page fee of EP applications is for each page in excess of 35, it is in PCT where it is 30.