You wouldn't like it if said company kept surprising you with new contract terms every time you've agreed on something. Especially in this stage of your relationship, it's best to be transparent and open about your requests.
There's also an added benefit to this transparancy; if the company is unable to meet one of your requests, let's say there's a maximum of two remote working days per week, they might compensate for it by increasing their salary offer. Chris Voss, an ex-FBI hostage negotiator, wrote a book called Never Split the Difference, which covers negotiating salary and contract terms. I found it a very useful book, and this excerpt might answer your question:
"...the more you talk about nonsalary terms, the more likely you are to hear the full range of their options. If they can’t meet your nonsalary requests, they may even counter with more money, like they did with a French-born American former student of mine. She kept asking — with a big smile — for an extra week of vacation beyond what the company normally gave. She was “French,” she said, and that’s what French people did. The hiring company was completely handcuffed on the vacation issue, but because she was so darned delightful, and because she introduced a nonmonetary variable into the notion of her value, they countered by increasing her salary offer."