I believe there a couple fo ways you can tackle you question, however it is important to keep in mind as to "what do you want to do with this data?". Basically if it is just for storage and edit, or maybe you would like to make some analysis? Below are a couple of possible solutions, since you were not precise on your use (how you wish to structure your data, ect), I am making broad approaches (links at the bottom):
1 - Use Cloud Provider + Document Editor: this is basically using Google Drive/OneDrive/Dropbox as your cloud repository and edit the files with both online and also client installations spreadsheets editor of your choice. You can go strictly Google Docs style, or maintain your Excel formats and use web excel (there are mobile apps for all of these platforms). I would not really recommend this, especially if you have a lot of data, but it is definitely an option.
2 - Use Document Management Software: like LogicalDOC, OpenKM, Alfresco, etc. There are OpenSource options for these. Now, they are not spreadsheet exclusive, they manage all types of documents and files. This is excellent for handling not just a very large quantity of files, but also a variety of file types. Some have editing capabilities, but for full feature you would have to go with the commercial options.
3 - Use Database: this would be my best choice. You have a variety of DataBase editors - MS Access, Libre Office Base, FileMaker Pro, among others - where you can have multiple types of databases, as well as custom fields, etc. Mobile access, use cloud service for access management, among other possible scenarios. Very flexible and customisable.
All of the above are basically for keeping the data in place, editing, updating and also sharing (managing access). Now, for data handling and also analysing, I would suggest:
4 - Use data analysis platform: Microsoft Power BI. This is a fantastic tool for data management and analysis. It can connect to excel, Access, among other database formats and online storage providers. Provides tools for analysis and reporting. Although you cannot edit via mobile, you can view reports and data sets. Other tools for analysis like Tableau are also great, however they do not have a Free version (only trial) for you to be able to get a hang of the platform.
If I have not helped you with a direct solution, I hope I at least assisted in guiding you to the right direction.
Below the links: