If you want to learn the Romance languages together, you need to use resources that compare the languages.
Romance language books written in English
One of the oldest books intended to help you learn the Romance languages together is Comparative Grammar of French, Italian, Spanish & Portuguese Languages by Edwin A. Notley. This book was published in 1868 so it’s in the public domain and you can download a PDF that I created. Since it is so old, however, there are few spellings and words that are no longer used in the contemporary languages, so you will need to augment your study with more recent materials. Some copies show up on amazon.com every once in a while, but at a ridiculous price ($1,500!)
The Loom of Language: An Approach to the Mastery of Many Languages by Frederick Bodmer actually compares four Romance languages (French, Italian, Spanish and Portuguese) as well as four Germanic languages (German, Dutch, Swedish and Danish), and offers advice on how to study multiple languages at the same time. Though a bit outdated, it is still my favorite book. You can get a copy at amazon.com for a relatively cheap price. I previously posted a review of this book if you’d like to know more.
The Seven Sieves: How to read all the Romance languages right away 
Another great book is Comparative Practical Grammar of French, Spanish and Italian by O.H. Heatwole. The main drawback is that there are only three languages, and since it’s out of print, it can be a bit difficult to find online. Third-party sellers do sell it on Amazon but it’s usually rather expensive.
Romance language books not written in English
EuRom5 (2011) is the most recent multilingual book I’ve seen yet. It focuses on learning to read and comprehend five Romance languages. The book is written in French, Italian, Spanish, Catalan and Portuguese (so it is designed for native/advanced users of any of those languages) with texts and audio files available on the website. You can buy it from dicoland.com or hoepli.it for under 30€. Amazon.fr also sells it for 30-40€ and a few copies are available on amazon.com. This book is not quite as “comparative” as the other books in the list since it offers 20 articles in one language with some words glossed in the other 4 languages (i.e. the entire articles are not translated in the other languages). You can also read my summary/review.
Comprendre les langues romanes: Du français à l’espagnol, au portugais, à l’italien & au roumain. Méthode d’intercompréhension by Paul Teyssier (2004) is obviously written in French for French-speakers to learn to comprehend Spanish, Portuguese, Italian, and Romanian. A new edition came out in 2012, but I don’t know if/how it is different from the 2004 edition, which is what I bought. Both editions are available via amazon.com or amazon.fr or you can order it from Librairie Portugaise & Brésilienne in Paris for 29€, and they do ship worldwide. I believe translations of this book in the other languages exist, but I’m not sure where to buy them.
Romance language resources at ielanguages.com
If you want to study vocabulary lists to learn the Romance languages, I have many lists available at Romance Languages Vocabulary Lists as well as some verb conjugations. The tables are set up so that English is first, followed by French, Italian, Spanish and then Portuguese. I chose this order due to how similar the languages are to each other. However, this may not be the order that you want to study the Romance languages in. Luckily, you can drag the columns in any order that you like! Simply click on the name of the language in the first column and drag it left or right. You can also hide/show languages that you are not studying or when you want to quickly test your memory. A few topics also have fill-in-the-blank exercises, such as days of the week:
Lastly, I’ve been creating videos that teach French, Italian, Spanish, and Portuguese together. (I have also created a few videos to teach French and Spanish together.) Subscribe to the Youtube channel to be notified when any new videos are available.
I am really interested in finding other books, websites, or videos that help you learn the Romance languages together. Has anyone found other useful resources?