relay triggering another relay

Hi, i installed a set of aftermarket horns to replace my one wimpy horn but with the stock relay they still arent that loud. i tried putting a different relay in place of stock but still the same. i tried using the stock relay to trigger the relay horns came with and it was MUCH louder.    My question is , is it safe/ok to have the stock relay trigger a second relay triggering the horns? Thanks :)

its on a 1996 nissan altima

Mount the trumpets inside the splash shield facing the road (down) installing them in the engine bay is a waste of time because the engine parts and installation muffle the sound. Also I'd use the original relay and if necessary upgrade the fuse, that's what I do and I've owned two Maximas and right now a smaller Nissan all with air horns.
If you piggy-back the second relay, (use the NEG horn push wire to trigger it), and you press the horn for a second or less,you get the original horns, hold the horn button longer for the air horns. Without the second relay it's instant.

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Amateurs assume, don't test and have problems; pros test first. I am not a free install service.
Read the installation manual, do a search here or online for your vehicle wiring before posting.

Keeping in mind the usual (traditional) "hot" relay with grounded horn-switch (ie, a 3-terminal relay, else "normal" with #30 & #86 connected together to +12V).
(I presume it's wired traditionally.)

I'd probably run a new fuse and heavier +12V power cable for the new horn(s), but that assumes it uses 4-terminal relay IF the horns only work with IGN (or ACC) on - ie, #86 of the new relay to "B" or +12V supply of the original relay, then #85 to the horn-switch (usually "S" on a 3-terminal horn relay) - unless you want the new horns to be usable at any time (then a 3-terminal horn relay or #86 to #30 as normal).